# naive search of \pm a^x1 \pm a^x2 = \pm b^y1 \pm b^y2  for a<b and biggest power up to 10^20
# Extending Cris Crawford's results
# 
# April 1, 2004
# 
# We find all solutions to \pm a^x1 \pm a^x2 = \pm b^y1 \pm b^y2  for a<b, 0<x1 < x2, 0<y1<y2, and the max of a^x2, b^y2 < 10^20, and a,b < 10000.
# 
# There are many infinite families.  The most trivial are when a and b are powers of a common base, so we only consider a and b that are not perfect powers.  
# 
# The next infinite family is when b = a+1 and we get  a^2 + a = (a+1)^2 - (a+1).  We eliminate this case below by not allowing y2=2 when b=a+1.  Actually, this restriction is not quite accurate, since it unfortunately misses two cases, the case  3^2 - 3 = 2^3 - 2 and the case  3^2+3 = 2^3 + 2^2.  See Lemma 6 of the paper.  
# 
# If either  a  or  a+1  is a perfect power, this infinite family appears in disguise, e.g.,  5^4 + 5^2 = 26^2 - 26, or 3^6 + 3^3 = 28^2 - 28, or 26^2 + 26 = 3^6 - 3^3.  We do not eliminate these because it is convenient to have something printing every so often to assure that the program is functioning.    
# 
# 
> restart;
> findpower := proc(a, bpart)
> local t, i, ans;
> ans := 0;
> t:= bpart;
> while t mod a = 0 do t := t/a; ans := ans + 1;
> od;
> ans;
> end; 
             findpower := proc(a, bpart)  ...  end; 
> findpower(2,28);
                               2 
> naive := proc(b)
> local a,x1,x2,y1,y2,temp,bplus,bminus;
> for y2 from 2 to round(20*log(10.0)/log(b)) do
> for y1 from 1 to y2-1 do
> bplus := b^y2 + b^y1;
> bminus := b^y2 - b^y1;
> for a from 2 to b-1 do
> if iperfpow(a) = FAIL then
> if (a<b-1 or y2>2) then  
> #this eliminates the infinite family with b=a+1 and x2=y2=2, x1=y1=1.
> if bplus mod a = 0 then
> x1 := findpower(a, bplus);
> temp := log( bplus + a^x1)/log(a);
> if abs( evalf(temp - round(temp)) ) < 0.001 then 
> x2 := round(temp);
> if a^x2 = bplus + a^x1 then print(a,x2,x1,b,y2,y1,mp_||a||"^"||x2||"-"||a||"^"||x1||"="||b||"^"|| y2||"+"||b||"^"||y1, time()); fi;
> fi;
> if bplus > a^x1 then
> temp := log( bplus - a^x1 )/log(a);
> if abs( evalf(temp - round(temp)) ) < 0.001 then 
> x2 := round(temp);
> if a^x2 = bplus - a^x1 then print(a,x2,x1,b,y2,y1,pp_||a||"^"||x2||"+"||a||"^"||x1||"="||b||"^"|| y2||"+"||b||"^"||y1, time()); fi;
> fi;
> fi;
> fi;
> if bminus mod a = 0 then
> x1 := findpower(a, bminus);
> temp := log( bminus + a^x1)/log(a);
> if abs( evalf(temp - round(temp)) ) < 0.001 then 
> x2 := round(temp);
> if a^x2 = bminus + a^x1 then print(a,x2,x1,b,y2,y1,mm_||a||"^"||x2||"-"||a||"^"||x1||"="||b||"^"|| y2||"-"||b||"^"||y1, time()); fi;
> fi;
> if bminus > a^x1 then
> temp := log( bminus - a^x1)/log(a);
> if abs( evalf(temp - round(temp)) ) < 0.001 then 
> x2 := round(temp);
> if a^x2 = bminus - a^x1 then print(a,x2,x1,b,y2,y1,pm_||a||"^"||x2||"+"||a||"^"||x1||"="||b||"^"|| y2||"-"||b||"^"||y1, time()); fi;
> fi;
> fi;
> fi;
> fi;
> fi;
> od;od;od; 
> end;
                  naive := proc(b)  ...  end; 
# 
# 
# 
# 
# 
# 
# Recall that the list below misses two special cases, 2^3 + 2^2 = 3^2 + 3  and  2^3 - 2 = 3^2 - 3.  
> for b from 3 to 5000 do
> if iperfpow(b) = FAIL then
> naive(b);
> fi;od;
              2, 5, 1, 3, 3, 1, mp_2^5-2^1=3^3+3^1                      
              2, 5, 3, 3, 3, 1, mm_2^5-2^3=3^3-3^1                      
              2, 4, 3, 3, 3, 1, pm_2^4+2^3=3^3-3^1                      
              2, 5, 2, 3, 3, 2, pp_2^5+2^2=3^3+3^2                      
              2, 4, 1, 3, 3, 2, pm_2^4+2^1=3^3-3^2                      
              2, 6, 3, 3, 4, 2, pm_2^6+2^3=3^4-3^2                      
              2, 8, 4, 3, 5, 1, mm_2^8-2^4=3^5-3^1                      
              2, 8, 2, 3, 5, 2, mp_2^8-2^2=3^5+3^2                      
              2, 5, 1, 5, 2, 1, mp_2^5-2^1=5^2+5^1                      
              2, 4, 2, 5, 2, 1, pm_2^4+2^2=5^2-5^1                      
              3, 3, 1, 5, 2, 1, pp_3^3+3^1=5^2+5^1                      
              2, 7, 1, 5, 3, 1, pp_2^7+2^1=5^3+5^1                      
              2, 7, 3, 5, 3, 1, mm_2^7-2^3=5^3-5^1                      
              2, 5, 1, 6, 2, 1, mm_2^5-2^1=6^2-6^1                      
              3, 3, 1, 6, 2, 1, pm_3^3+3^1=6^2-6^1                      
              2, 8, 2, 6, 3, 2, mp_2^8-2^2=6^3+6^2                      
              3, 5, 2, 6, 3, 2, pp_3^5+3^2=6^3+6^2                      
              3, 8, 4, 6, 5, 4, mm_3^8-3^4=6^5-6^4                      
              2, 6, 3, 7, 2, 1, mp_2^6-2^3=7^2+7^1                      
            3, 4, 2, 10, 2, 1, pm_3^4+3^2=10^2-10^1                      
            2, 7, 2, 11, 2, 1, pp_2^7+2^2=11^2+11^1                      
            2, 7, 2, 12, 2, 1, pm_2^7+2^2=12^2-12^1                      
            3, 7, 1, 13, 3, 1, mm_3^7-3^1=13^3-13^1                      
            6, 3, 1, 14, 2, 1, mp_6^3-6^1=14^2+14^1                      
            2, 8, 4, 15, 2, 1, mp_2^8-2^4=15^2+15^1                      
            3, 5, 1, 15, 2, 1, mp_3^5-3^1=15^2+15^1                      
            6, 3, 1, 15, 2, 1, mm_6^3-6^1=15^2-15^1                      
            5, 5, 2, 15, 3, 2, pm_5^5+5^2=15^3-15^2                      
            2, 8, 4, 17, 2, 1, pm_2^8+2^4=17^2-17^1                      
            5, 4, 2, 24, 2, 1, mp_5^4-5^2=24^2+24^1                      
            3, 6, 3, 26, 2, 1, mp_3^6-3^3=26^2+26^1                      
            5, 4, 2, 26, 2, 1, pm_5^4+5^2=26^2-26^1                      
            3, 6, 3, 28, 2, 1, pm_3^6+3^3=28^2-28^1                      
           2, 10, 5, 31, 2, 1, mp_2^10-2^5=31^2+31^1                      
           2, 10, 5, 33, 2, 1, pm_2^10+2^5=33^2-33^1                      
            6, 4, 2, 35, 2, 1, mp_6^4-6^2=35^2+35^1                      
            6, 4, 2, 37, 2, 1, pm_6^4+6^2=37^2-37^1                      
           2, 16, 6, 40, 3, 2, pp_2^16+2^6=40^3+40^2                      
            7, 4, 2, 48, 2, 1, mp_7^4-7^2=48^2+48^1                      
            7, 4, 2, 50, 2, 1, pm_7^4+7^2=50^2-50^1                      
           35, 2, 2, 50, 2, 1, pm_35^2+35^2=50^2-50^1                      
           2, 12, 6, 63, 2, 1, mp_2^12-2^6=63^2+63^1                      
           2, 12, 6, 65, 2, 1, pm_2^12+2^6=65^2-65^1                      
            3, 8, 4, 80, 2, 1, mp_3^8-3^4=80^2+80^1                      
            6, 5, 4, 80, 2, 1, mp_6^5-6^4=80^2+80^1                      
            3, 8, 4, 82, 2, 1, pm_3^8+3^4=82^2-82^1                      
           2, 13, 1, 90, 2, 1, mp_2^13-2^1=90^2+90^1                      
           2, 13, 1, 91, 2, 1, mm_2^13-2^1=91^2-91^1                      
           21, 3, 2, 98, 2, 1, pp_21^3+21^2=98^2+98^1                      
           10, 4, 2, 99, 2, 1, mp_10^4-10^2=99^2+99^1                      
           21, 3, 2, 99, 2, 1, pm_21^3+21^2=99^2-99^1                      
         10, 4, 2, 101, 2, 1, pm_10^4+10^2=101^2-101^1                      
         11, 4, 2, 120, 2, 1, mp_11^4-11^2=120^2+120^1                      
         11, 4, 2, 122, 2, 1, pm_11^4+11^2=122^2-122^1                      
           5, 6, 3, 124, 2, 1, mp_5^6-5^3=124^2+124^1                      
           5, 6, 3, 126, 2, 1, pm_5^6+5^3=126^2-126^1                      
          2, 14, 7, 127, 2, 1, mp_2^14-2^7=127^2+127^1                      
          2, 14, 7, 129, 2, 1, pm_2^14+2^7=129^2-129^1                      
         12, 4, 2, 143, 2, 1, mp_12^4-12^2=143^2+143^1                      
         12, 4, 2, 145, 2, 1, pm_12^4+12^2=145^2-145^1                      
         13, 4, 2, 168, 2, 1, mp_13^4-13^2=168^2+168^1                      
         13, 4, 2, 170, 2, 1, pm_13^4+13^2=170^2-170^1                      
         14, 4, 2, 195, 2, 1, mp_14^4-14^2=195^2+195^1                      
         14, 4, 2, 197, 2, 1, pm_14^4+14^2=197^2-197^1                      
# aborted here.  Start again, adding a time stamp
> for b from 197 to 5000 do
> if iperfpow(b) = FAIL then
> naive(b);
> fi;od;
      14, 4, 2, 197, 2, 1, pm_14^4+14^2=197^2-197^1, 1.327                      
      6, 6, 3, 215, 2, 1, mp_6^6-6^3=215^2+215^1, 474.458                      
      6, 6, 3, 217, 2, 1, pm_6^6+6^3=217^2-217^1, 502.159                      
     15, 4, 2, 224, 2, 1, mp_15^4-15^2=224^2+224^1, 696.629                      
     15, 4, 2, 226, 2, 1, pm_15^4+15^2=226^2-226^1, 730.006                      
     3, 10, 5, 242, 2, 1, mp_3^10-3^5=242^2+242^1, 1061.585                      
     3, 10, 5, 244, 2, 1, pm_3^10+3^5=244^2-244^1, 1080.445                      
     2, 16, 8, 255, 2, 1, mp_2^16-2^8=255^2+255^1, 1331.836                      
     2, 16, 8, 257, 2, 1, pm_2^16+2^8=257^2-257^1, 1365.509                      
      5, 7, 1, 279, 2, 1, mp_5^7-5^1=279^2+279^1, 1872.772                      
      5, 7, 1, 280, 2, 1, mm_5^7-5^1=280^2-280^1, 1901.098                      
    17, 4, 2, 288, 2, 1, mp_17^4-17^2=288^2+288^1, 2105.736                      
   204, 2, 2, 288, 2, 1, pp_204^2+204^2=288^2+288^1, 2106.220                      
    17, 4, 2, 290, 2, 1, pm_17^4+17^2=290^2-290^1, 2135.799                      
    18, 4, 2, 323, 2, 1, mp_18^4-18^2=323^2+323^1, 2980.620                      
    18, 4, 2, 325, 2, 1, pm_18^4+18^2=325^2-325^1, 3008.090                      
      7, 6, 3, 342, 2, 1, mp_7^6-7^3=342^2+342^1, 3462.227                      
      7, 6, 3, 344, 2, 1, pm_7^6+7^3=344^2-344^1, 3500.667                      
    19, 4, 2, 360, 2, 1, mp_19^4-19^2=360^2+360^1, 3924.595                      
    19, 4, 2, 362, 2, 1, pm_19^4+19^2=362^2-362^1, 3969.767                      
    20, 4, 2, 399, 2, 1, mp_20^4-20^2=399^2+399^1, 5054.858                      
    20, 4, 2, 401, 2, 1, pm_20^4+20^2=401^2-401^1, 5101.203                      
    21, 4, 2, 440, 2, 1, mp_21^4-21^2=440^2+440^1, 6311.499                      
    21, 4, 2, 442, 2, 1, pm_21^4+21^2=442^2-442^1, 6364.266                      
    22, 4, 2, 483, 2, 1, mp_22^4-22^2=483^2+483^1, 7542.954                      
    22, 4, 2, 485, 2, 1, pm_22^4+22^2=485^2-485^1, 7573.904                      
     2, 18, 9, 511, 2, 1, mp_2^18-2^9=511^2+511^1, 8211.759                      
     2, 18, 9, 513, 2, 1, pm_2^18+2^9=513^2-513^1, 8238.226                      
    23, 4, 2, 528, 2, 1, mp_23^4-23^2=528^2+528^1, 8602.950                      
    23, 4, 2, 530, 2, 1, pm_23^4+23^2=530^2-530^1, 8643.102                      
    24, 4, 2, 575, 2, 1, mp_24^4-24^2=575^2+575^1, 9837.205                      
    24, 4, 2, 577, 2, 1, pm_24^4+24^2=577^2-577^1, 9871.642                      
     5, 8, 4, 624, 2, 1, mp_5^8-5^4=624^2+624^1, 11157.824                      
     5, 8, 4, 626, 2, 1, pm_5^8+5^4=626^2-626^1, 11202.900                      
    26, 4, 2, 675, 2, 1, mp_26^4-26^2=675^2+675^1, 12642.876                      
    26, 4, 2, 677, 2, 1, pm_26^4+26^2=677^2-677^1, 12677.469                      
    3, 12, 6, 728, 2, 1, mp_3^12-3^6=728^2+728^1, 14239.828                      
    3, 12, 6, 730, 2, 1, pm_3^12+3^6=730^2-730^1, 14278.263                      
    28, 4, 2, 783, 2, 1, mp_28^4-28^2=783^2+783^1, 16028.736                      
    28, 4, 2, 785, 2, 1, pm_28^4+28^2=785^2-785^1, 16073.843                      
    29, 4, 2, 840, 2, 1, mp_29^4-29^2=840^2+840^1, 17916.633                      
    29, 4, 2, 842, 2, 1, pm_29^4+29^2=842^2-842^1, 17982.755                      
    30, 4, 2, 899, 2, 1, mp_30^4-30^2=899^2+899^1, 19987.741                      
    30, 4, 2, 901, 2, 1, pm_30^4+30^2=901^2-901^1, 20023.352                      
    31, 4, 2, 960, 2, 1, mp_31^4-31^2=960^2+960^1, 22214.327                      
    31, 4, 2, 962, 2, 1, pm_31^4+31^2=962^2-962^1, 22270.824                      
    10, 6, 3, 999, 2, 1, mp_10^6-10^3=999^2+999^1, 23657.109                      
  10, 6, 3, 1001, 2, 1, pm_10^6+10^3=1001^2-1001^1, 23700.578                      
  2, 20, 10, 1023, 2, 1, mp_2^20-2^10=1023^2+1023^1, 24555.989                      
  2, 20, 10, 1025, 2, 1, pm_2^20+2^10=1025^2-1025^1, 24607.488                      
  33, 4, 2, 1088, 2, 1, mp_33^4-33^2=1088^2+1088^1, 27256.716                      
  33, 4, 2, 1090, 2, 1, pm_33^4+33^2=1090^2-1090^1, 27299.650                      
  34, 4, 2, 1155, 2, 1, mp_34^4-34^2=1155^2+1155^1, 30090.696                      
  34, 4, 2, 1157, 2, 1, pm_34^4+34^2=1157^2-1157^1, 30169.978                      
  35, 4, 2, 1224, 2, 1, mp_35^4-35^2=1224^2+1224^1, 32767.782                      
  35, 4, 2, 1226, 2, 1, pm_35^4+35^2=1226^2-1226^1, 32817.752                      
    6, 8, 4, 1295, 2, 1, mp_6^8-6^4=1295^2+1295^1, 34996.142                      
    6, 8, 4, 1297, 2, 1, pm_6^8+6^4=1297^2-1297^1, 35043.624                      
  11, 6, 3, 1330, 2, 1, mp_11^6-11^3=1330^2+1330^1, 36086.123                      
  11, 6, 3, 1332, 2, 1, pm_11^6+11^3=1332^2-1332^1, 36131.513                      
  37, 4, 2, 1368, 2, 1, mp_37^4-37^2=1368^2+1368^1, 37365.382                      
  37, 4, 2, 1370, 2, 1, pm_37^4+37^2=1370^2-1370^1, 37404.741                      
  38, 4, 2, 1443, 2, 1, mp_38^4-38^2=1443^2+1443^1, 39940.197                      
  38, 4, 2, 1445, 2, 1, pm_38^4+38^2=1445^2-1445^1, 39982.740                      
  39, 4, 2, 1520, 2, 1, mp_39^4-39^2=1520^2+1520^1, 42725.792                      
  39, 4, 2, 1522, 2, 1, pm_39^4+39^2=1522^2-1522^1, 42788.685                      
Warning,  computation interrupted
> b;
                              1566                      
> for b from 1566 to 10000 do
> if iperfpow(b) = FAIL then
> naive(b);
> fi;od;
   40, 4, 2, 1599, 2, 1, mp_40^4-40^2=1599^2+1599^1, 1365.663                     
   40, 4, 2, 1601, 2, 1, pm_40^4+40^2=1601^2-1601^1, 1424.695                     
   41, 4, 2, 1680, 2, 1, mp_41^4-41^2=1680^2+1680^1, 4588.038                     
   41, 4, 2, 1682, 2, 1, pm_41^4+41^2=1682^2-1682^1, 4667.492                     
1189, 2, 2, 1682, 2, 1, pm_1189^2+1189^2=1682^2-1682^1, 4668.632                     
   12, 6, 3, 1727, 2, 1, mp_12^6-12^3=1727^2+1727^1, 6509.341                     
   12, 6, 3, 1729, 2, 1, pm_12^6+12^3=1729^2-1729^1, 6548.136                     
   42, 4, 2, 1763, 2, 1, mp_42^4-42^2=1763^2+1763^1, 7961.058                     
   42, 4, 2, 1765, 2, 1, pm_42^4+42^2=1765^2-1765^1, 8000.278                     
  43, 4, 2, 1848, 2, 1, mp_43^4-43^2=1848^2+1848^1, 11627.469                     
  43, 4, 2, 1850, 2, 1, pm_43^4+43^2=1850^2-1850^1, 11689.549                     
  44, 4, 2, 1935, 2, 1, mp_44^4-44^2=1935^2+1935^1, 15566.494                     
  44, 4, 2, 1937, 2, 1, pm_44^4+44^2=1937^2-1937^1, 15632.044                     
  45, 4, 2, 2024, 2, 1, mp_45^4-45^2=2024^2+2024^1, 19665.119                     
  45, 4, 2, 2026, 2, 1, pm_45^4+45^2=2026^2-2026^1, 19743.180                     
  2, 22, 11, 2047, 2, 1, mp_2^22-2^11=2047^2+2047^1, 20699.753                     
  2, 22, 11, 2049, 2, 1, pm_2^22+2^11=2049^2-2049^1, 20743.552                     
  46, 4, 2, 2115, 2, 1, mp_46^4-46^2=2115^2+2115^1, 24006.789                     
  46, 4, 2, 2117, 2, 1, pm_46^4+46^2=2117^2-2117^1, 24070.851                     
   3, 14, 7, 2186, 2, 1, mp_3^14-3^7=2186^2+2186^1, 27540.199                     
   3, 14, 7, 2188, 2, 1, pm_3^14+3^7=2188^2-2188^1, 27583.107                     
  13, 6, 3, 2196, 2, 1, mp_13^6-13^3=2196^2+2196^1, 27964.640                     
  13, 6, 3, 2198, 2, 1, pm_13^6+13^3=2198^2-2198^1, 28024.234                     
  47, 4, 2, 2208, 2, 1, mp_47^4-47^2=2208^2+2208^1, 28536.038                     
  47, 4, 2, 2210, 2, 1, pm_47^4+47^2=2210^2-2210^1, 28587.179                     
  48, 4, 2, 2303, 2, 1, mp_48^4-48^2=2303^2+2303^1, 33447.207                     
  48, 4, 2, 2305, 2, 1, pm_48^4+48^2=2305^2-2305^1, 33498.818                     
    7, 8, 4, 2400, 2, 1, mp_7^8-7^4=2400^2+2400^1, 38527.816                     
    7, 8, 4, 2402, 2, 1, pm_7^8+7^4=2402^2-2402^1, 38602.334                     
  50, 4, 2, 2499, 2, 1, mp_50^4-50^2=2499^2+2499^1, 43997.168                     
  50, 4, 2, 2501, 2, 1, pm_50^4+50^2=2501^2-2501^1, 44066.651                     
  51, 4, 2, 2600, 2, 1, mp_51^4-51^2=2600^2+2600^1, 49693.691                     
  51, 4, 2, 2602, 2, 1, pm_51^4+51^2=2602^2-2602^1, 49779.034                     
  52, 4, 2, 2703, 2, 1, mp_52^4-52^2=2703^2+2703^1, 55782.784                     
  52, 4, 2, 2705, 2, 1, pm_52^4+52^2=2705^2-2705^1, 55855.349                     
  14, 6, 3, 2743, 2, 1, mp_14^6-14^3=2743^2+2743^1, 58133.317                     
  14, 6, 3, 2745, 2, 1, pm_14^6+14^3=2745^2-2745^1, 58189.085                     
  53, 4, 2, 2808, 2, 1, mp_53^4-53^2=2808^2+2808^1, 62107.402                     
  53, 4, 2, 2810, 2, 1, pm_53^4+53^2=2810^2-2810^1, 62183.415                     
  54, 4, 2, 2915, 2, 1, mp_54^4-54^2=2915^2+2915^1, 68819.076                     
  54, 4, 2, 2917, 2, 1, pm_54^4+54^2=2917^2-2917^1, 68903.026                     
  55, 4, 2, 3024, 2, 1, mp_55^4-55^2=3024^2+3024^1, 75896.325                     
  55, 4, 2, 3026, 2, 1, pm_55^4+55^2=3026^2-3026^1, 76006.635                     
   5, 10, 5, 3124, 2, 1, mp_5^10-5^5=3124^2+3124^1, 82543.061                     
   5, 10, 5, 3126, 2, 1, pm_5^10+5^5=3126^2-3126^1, 82617.404                     
  56, 4, 2, 3135, 2, 1, mp_56^4-56^2=3135^2+3135^1, 83246.080                     
  56, 4, 2, 3137, 2, 1, pm_56^4+56^2=3137^2-3137^1, 83359.283                     
  57, 4, 2, 3248, 2, 1, mp_57^4-57^2=3248^2+3248^1, 91071.394                     
  57, 4, 2, 3250, 2, 1, pm_57^4+57^2=3250^2-3250^1, 91161.896                     
  58, 4, 2, 3363, 2, 1, mp_58^4-58^2=3363^2+3363^1, 99300.772                     
  58, 4, 2, 3365, 2, 1, pm_58^4+58^2=3365^2-3365^1, 99374.129                     
                                                               5

15, 6, 3, 3374, 2, 1, mp_15^6-15^3=3374^2+3374^1, 1.00017970 10                      
                                                               5

15, 6, 3, 3376, 2, 1, pm_15^6+15^3=3376^2-3376^1, 1.00094155 10                      
                                                               5

59, 4, 2, 3480, 2, 1, mp_59^4-59^2=3480^2+3480^1, 1.07899358 10                      
                                                               5

59, 4, 2, 3482, 2, 1, pm_59^4+59^2=3482^2-3482^1, 1.08013795 10                      
                                                               5

60, 4, 2, 3599, 2, 1, mp_60^4-60^2=3599^2+3599^1, 1.16955402 10                      
                                                               5

60, 4, 2, 3601, 2, 1, pm_60^4+60^2=3601^2-3601^1, 1.17040106 10                      
                                                               5

61, 4, 2, 3720, 2, 1, mp_61^4-61^2=3720^2+3720^1, 1.26332347 10                      
                                                               5

61, 4, 2, 3722, 2, 1, pm_61^4+61^2=3722^2-3722^1, 1.26426507 10                      
                                                               5

62, 4, 2, 3843, 2, 1, mp_62^4-62^2=3843^2+3843^1, 1.36307622 10                      
                                                               5

62, 4, 2, 3845, 2, 1, pm_62^4+62^2=3845^2-3845^1, 1.36407745 10                      
                                                               5

63, 4, 2, 3968, 2, 1, mp_63^4-63^2=3968^2+3968^1, 1.46594356 10                      
                                                               5

63, 4, 2, 3970, 2, 1, pm_63^4+63^2=3970^2-3970^1, 1.46685700 10                      
                                                                5

2, 24, 12, 4095, 2, 1, mp_2^24-2^12=4095^2+4095^1, 1.57458429 10                      
                                                                5

2, 24, 12, 4097, 2, 1, pm_2^24+2^12=4097^2-4097^1, 1.57609914 10                      
                                                               5

65, 4, 2, 4224, 2, 1, mp_65^4-65^2=4224^2+4224^1, 1.68693538 10                      
                                                               5

65, 4, 2, 4226, 2, 1, pm_65^4+65^2=4226^2-4226^1, 1.68825641 10                      
                                                               5

66, 4, 2, 4355, 2, 1, mp_66^4-66^2=4355^2+4355^1, 1.79578617 10                      
                                                               5

66, 4, 2, 4357, 2, 1, pm_66^4+66^2=4357^2-4357^1, 1.79652082 10                      
                                                               5

67, 4, 2, 4488, 2, 1, mp_67^4-67^2=4488^2+4488^1, 1.87390844 10                      
                                                               5

67, 4, 2, 4490, 2, 1, pm_67^4+67^2=4490^2-4490^1, 1.87468700 10                      
                                                               5

68, 4, 2, 4623, 2, 1, mp_68^4-68^2=4623^2+4623^1, 1.95554780 10                      
                                                               5

68, 4, 2, 4625, 2, 1, pm_68^4+68^2=4625^2-4625^1, 1.95620981 10                      
                                                               5

69, 4, 2, 4760, 2, 1, mp_69^4-69^2=4760^2+4760^1, 2.04042794 10                      
                                                               5

69, 4, 2, 4762, 2, 1, pm_69^4+69^2=4762^2-4762^1, 2.04130731 10                      
                                                               5

70, 4, 2, 4899, 2, 1, mp_70^4-70^2=4899^2+4899^1, 2.12885842 10                      
                                                               5

70, 4, 2, 4901, 2, 1, pm_70^4+70^2=4901^2-4901^1, 2.12964607 10                      
                                                               5

17, 6, 3, 4912, 2, 1, mp_17^6-17^3=4912^2+4912^1, 2.13639013 10                      
                                                               5

17, 6, 3, 4914, 2, 1, pm_17^6+17^3=4914^2-4914^1, 2.13694544 10                      
                                                               5

30, 5, 1, 4929, 2, 1, mp_30^5-30^1=4929^2+4929^1, 2.14683653 10                      
                                                               5

30, 5, 1, 4930, 2, 1, mm_30^5-30^1=4930^2-4930^1, 2.14776526 10                      
                                                               5

71, 4, 2, 5040, 2, 1, mp_71^4-71^2=5040^2+5040^1, 2.22001055 10                      
                                                               5

71, 4, 2, 5042, 2, 1, pm_71^4+71^2=5042^2-5042^1, 2.22095959 10                      
                                                               5

72, 4, 2, 5183, 2, 1, mp_72^4-72^2=5183^2+5183^1, 2.31570580 10                      
                                                               5

72, 4, 2, 5185, 2, 1, pm_72^4+72^2=5185^2-5185^1, 2.31634756 10                      
                                                               5

73, 4, 2, 5328, 2, 1, mp_73^4-73^2=5328^2+5328^1, 2.41512929 10                      
                                                               5

73, 4, 2, 5330, 2, 1, pm_73^4+73^2=5330^2-5330^1, 2.41589332 10                      
                                                               5

74, 4, 2, 5475, 2, 1, mp_74^4-74^2=5475^2+5475^1, 2.51853675 10                      
                                                               5

74, 4, 2, 5477, 2, 1, pm_74^4+74^2=5477^2-5477^1, 2.51941426 10                      
                                                               5

75, 4, 2, 5624, 2, 1, mp_75^4-75^2=5624^2+5624^1, 2.62589006 10                      
                                                               5

75, 4, 2, 5626, 2, 1, pm_75^4+75^2=5626^2-5626^1, 2.62672555 10                      
                                                               5

76, 4, 2, 5775, 2, 1, mp_76^4-76^2=5775^2+5775^1, 2.73746885 10                      
                                                               5

76, 4, 2, 5777, 2, 1, pm_76^4+76^2=5777^2-5777^1, 2.73858303 10                      
                                                               5

18, 6, 3, 5831, 2, 1, mp_18^6-18^3=5831^2+5831^1, 2.77918269 10                      
                                                               5

18, 6, 3, 5833, 2, 1, pm_18^6+18^3=5833^2-5833^1, 2.78012814 10                      
                                                               5

77, 4, 2, 5928, 2, 1, mp_77^4-77^2=5928^2+5928^1, 2.85223946 10                      
                                                               5

77, 4, 2, 5930, 2, 1, pm_77^4+77^2=5930^2-5930^1, 2.85337007 10                      
                                                               5

78, 4, 2, 6083, 2, 1, mp_78^4-78^2=6083^2+6083^1, 2.97237589 10                      
                                                               5

78, 4, 2, 6085, 2, 1, pm_78^4+78^2=6085^2-6085^1, 2.97322992 10                      
                                                               5

79, 4, 2, 6240, 2, 1, mp_79^4-79^2=6240^2+6240^1, 3.09692141 10                      
                                                               5

79, 4, 2, 6242, 2, 1, pm_79^4+79^2=6242^2-6242^1, 3.09800540 10                      
                                                               5

80, 4, 2, 6399, 2, 1, mp_80^4-80^2=6399^2+6399^1, 3.22578374 10                      
                                                               5

80, 4, 2, 6401, 2, 1, pm_80^4+80^2=6401^2-6401^1, 3.22668965 10                      
                                                              5

3, 16, 8, 6560, 2, 1, mp_3^16-3^8=6560^2+6560^1, 3.35948267 10                      
                                                              5

3, 16, 8, 6562, 2, 1, pm_3^16+3^8=6562^2-6562^1, 3.36048331 10                      
                                                               5

82, 4, 2, 6723, 2, 1, mp_82^4-82^2=6723^2+6723^1, 3.49825591 10                      
                                                               5

82, 4, 2, 6725, 2, 1, pm_82^4+82^2=6725^2-6725^1, 3.49906138 10                      
Warning,  computation interrupted
> b;
                              6749                     
> for b from 6749 to 10000 do
> if iperfpow(b) = FAIL then
> naive(b);
> fi;od;
   19, 6, 3, 6858, 2, 1, mp_19^6-19^3=6858^2+6858^1, 9556.392                   
   19, 6, 3, 6860, 2, 1, pm_19^6+19^3=6860^2-6860^1, 9637.672                   
  83, 4, 2, 6888, 2, 1, mp_83^4-83^2=6888^2+6888^1, 12119.285                   
  83, 4, 2, 6890, 2, 1, pm_83^4+83^2=6890^2-6890^1, 12225.443                   
  84, 4, 2, 7055, 2, 1, mp_84^4-84^2=7055^2+7055^1, 27678.164                   
  84, 4, 2, 7057, 2, 1, pm_84^4+84^2=7057^2-7057^1, 27788.804                   
  85, 4, 2, 7224, 2, 1, mp_85^4-85^2=7224^2+7224^1, 43628.583                   
  85, 4, 2, 7226, 2, 1, pm_85^4+85^2=7226^2-7226^1, 43763.581                   
  86, 4, 2, 7395, 2, 1, mp_86^4-86^2=7395^2+7395^1, 60101.054                   
  86, 4, 2, 7397, 2, 1, pm_86^4+86^2=7397^2-7397^1, 60209.306                   
  87, 4, 2, 7568, 2, 1, mp_87^4-87^2=7568^2+7568^1, 77067.585                   
  87, 4, 2, 7570, 2, 1, pm_87^4+87^2=7570^2-7570^1, 77189.676                   
  88, 4, 2, 7743, 2, 1, mp_88^4-88^2=7743^2+7743^1, 94554.259                   
  88, 4, 2, 7745, 2, 1, pm_88^4+88^2=7745^2-7745^1, 94673.463                   
   6, 10, 5, 7775, 2, 1, mp_6^10-6^5=7775^2+7775^1, 98182.060                   
   6, 10, 5, 7777, 2, 1, pm_6^10+6^5=7777^2-7777^1, 98395.009                   
                                                               5

89, 4, 2, 7920, 2, 1, mp_89^4-89^2=7920^2+7920^1, 1.13181069 10                    
                                                               5

89, 4, 2, 7922, 2, 1, pm_89^4+89^2=7922^2-7922^1, 1.13315756 10                    
                                                               5

20, 6, 3, 7999, 2, 1, mp_20^6-20^3=7999^2+7999^1, 1.21091837 10                    
                                                               5

20, 6, 3, 8001, 2, 1, pm_20^6+20^3=8001^2-8001^1, 1.21195227 10                    
Warning,  computation interrupted
> b;
                              8013                   
> for b from 8013 to 25000 do
> if iperfpow(b) = FAIL then
> naive(b);
> fi;od;
   90, 4, 2, 8099, 2, 1, mp_90^4-90^2=8099^2+8099^1, 8998.859                 
   90, 4, 2, 8101, 2, 1, pm_90^4+90^2=8101^2-8101^1, 9120.328                 
  2, 26, 13, 8191, 2, 1, mp_2^26-2^13=8191^2+8191^1, 18625.094                 
  2, 26, 13, 8193, 2, 1, pm_2^26+2^13=8193^2-8193^1, 18726.903                 
  91, 4, 2, 8280, 2, 1, mp_91^4-91^2=8280^2+8280^1, 27934.263                 
  91, 4, 2, 8282, 2, 1, pm_91^4+91^2=8282^2-8282^1, 28102.609                 
  92, 4, 2, 8463, 2, 1, mp_92^4-92^2=8463^2+8463^1, 47691.159                 
  92, 4, 2, 8465, 2, 1, pm_92^4+92^2=8465^2-8465^1, 47822.485                 
  93, 4, 2, 8648, 2, 1, mp_93^4-93^2=8648^2+8648^1, 68045.914                 
  93, 4, 2, 8650, 2, 1, pm_93^4+93^2=8650^2-8650^1, 68159.778                 
  94, 4, 2, 8835, 2, 1, mp_94^4-94^2=8835^2+8835^1, 88919.479                 
  94, 4, 2, 8837, 2, 1, pm_94^4+94^2=8837^2-8837^1, 89054.618                 
                                                               5

95, 4, 2, 9024, 2, 1, mp_95^4-95^2=9024^2+9024^1, 1.10605168 10                  
                                                               5

95, 4, 2, 9026, 2, 1, pm_95^4+95^2=9026^2-9026^1, 1.10740103 10                  
                                                               5

96, 4, 2, 9215, 2, 1, mp_96^4-96^2=9215^2+9215^1, 1.32865981 10                  
                                                               5

96, 4, 2, 9217, 2, 1, pm_96^4+96^2=9217^2-9217^1, 1.32997323 10                  
                                                               5

21, 6, 3, 9260, 2, 1, mp_21^6-21^3=9260^2+9260^1, 1.37978357 10                  
                                                               5

21, 6, 3, 9262, 2, 1, pm_21^6+21^3=9262^2-9262^1, 1.38110155 10                  
                                                               5

97, 4, 2, 9408, 2, 1, mp_97^4-97^2=9408^2+9408^1, 1.55611746 10                  
                                                               5

97, 4, 2, 9410, 2, 1, pm_97^4+97^2=9410^2-9410^1, 1.55753101 10                  
                                                               5

98, 4, 2, 9603, 2, 1, mp_98^4-98^2=9603^2+9603^1, 1.79187797 10                  
                                                               5

98, 4, 2, 9605, 2, 1, pm_98^4+98^2=9605^2-9605^1, 1.79318357 10                  
                                                               5

99, 4, 2, 9800, 2, 1, mp_99^4-99^2=9800^2+9800^1, 2.03385500 10                  
                                                                     5

6930, 2, 2, 9800, 2, 1, pp_6930^2+6930^2=9800^2+9800^1, 2.03395501 10                  
                                                               5

99, 4, 2, 9802, 2, 1, pm_99^4+99^2=9802^2-9802^1, 2.03556176 10                  
                                                               5

10, 8, 4, 9999, 2, 1, mp_10^8-10^4=9999^2+9999^1, 2.28365830 10                  
                                                                  5

10, 8, 4, 10001, 2, 1, pm_10^8+10^4=10001^2-10001^1, 2.28508905 10                  
Warning,  computation interrupted
> b;
                             10186                 
> for b from 10186 to 25000 do
> if iperfpow(b) = FAIL then
> naive(b);
> fi;od;
101, 4, 2, 10200, 2, 1, mp_101^4-101^2=10200^2+10200^1, 1727.465                
101, 4, 2, 10202, 2, 1, pm_101^4+101^2=10202^2-10202^1, 1909.717                
102, 4, 2, 10403, 2, 1, mp_102^4-102^2=10403^2+10403^1, 27610.354                
102, 4, 2, 10405, 2, 1, pm_102^4+102^2=10405^2-10405^1, 27732.145                
103, 4, 2, 10608, 2, 1, mp_103^4-103^2=10608^2+10608^1, 53733.556                
103, 4, 2, 10610, 2, 1, pm_103^4+103^2=10610^2-10610^1, 53877.480                
Warning,  computation interrupted
> b;
                             10618                
> for b from 10618 to 25000 do
> if iperfpow(b) = FAIL then
> naive(b);
> fi;od;
 22, 6, 3, 10647, 2, 1, mp_22^6-22^3=10647^2+10647^1, 4443.663              
 22, 6, 3, 10649, 2, 1, pm_22^6+22^3=10649^2-10649^1, 4589.729              
104, 4, 2, 10815, 2, 1, mp_104^4-104^2=10815^2+10815^1, 25958.280              
104, 4, 2, 10817, 2, 1, pm_104^4+104^2=10817^2-10817^1, 26121.129              
105, 4, 2, 11024, 2, 1, mp_105^4-105^2=11024^2+11024^1, 53276.597              
105, 4, 2, 11026, 2, 1, pm_105^4+105^2=11026^2-11026^1, 53447.468              
106, 4, 2, 11235, 2, 1, mp_106^4-106^2=11235^2+11235^1, 81340.813              
106, 4, 2, 11237, 2, 1, pm_106^4+106^2=11237^2-11237^1, 81498.999              
                                                                     5

107, 4, 2, 11448, 2, 1, mp_107^4-107^2=11448^2+11448^1, 1.10237380 10               
                                                                     5

107, 4, 2, 11450, 2, 1, pm_107^4+107^2=11450^2-11450^1, 1.10379193 10               
                                                                     5

108, 4, 2, 11663, 2, 1, mp_108^4-108^2=11663^2+11663^1, 1.39976443 10               
                                                                     5

108, 4, 2, 11665, 2, 1, pm_108^4+108^2=11665^2-11665^1, 1.40116622 10               
                                                                     5

109, 4, 2, 11880, 2, 1, mp_109^4-109^2=11880^2+11880^1, 1.70312517 10               
                                                                     5

109, 4, 2, 11882, 2, 1, pm_109^4+109^2=11882^2-11882^1, 1.70497985 10               
                                                                     5

110, 4, 2, 12099, 2, 1, mp_110^4-110^2=12099^2+12099^1, 2.01612802 10               
                                                                     5

110, 4, 2, 12101, 2, 1, pm_110^4+110^2=12101^2-12101^1, 2.01768934 10               
                                                                  5

23, 6, 3, 12166, 2, 1, mp_23^6-23^3=12166^2+12166^1, 2.11175168 10               
                                                                  5

23, 6, 3, 12168, 2, 1, pm_23^6+23^3=12168^2-12168^1, 2.11328903 10               
                                                                     5

111, 4, 2, 12320, 2, 1, mp_111^4-111^2=12320^2+12320^1, 2.33528054 10               
                                                                     5

111, 4, 2, 12322, 2, 1, pm_111^4+111^2=12322^2-12322^1, 2.33735447 10               
Warning,  computation interrupted
> b;
                             12355              
> for b from 12355 to 25000 do
> if iperfpow(b) = FAIL then
> naive(b);
> fi;od;
112, 4, 2, 12543, 2, 1, mp_112^4-112^2=12543^2+12543^1, 27989.658             
112, 4, 2, 12545, 2, 1, pm_112^4+112^2=12545^2-12545^1, 28141.268             
113, 4, 2, 12768, 2, 1, mp_113^4-113^2=12768^2+12768^1, 61571.710             
113, 4, 2, 12770, 2, 1, pm_113^4+113^2=12770^2-12770^1, 61754.021             
114, 4, 2, 12995, 2, 1, mp_114^4-114^2=12995^2+12995^1, 96125.592             
114, 4, 2, 12997, 2, 1, pm_114^4+114^2=12997^2-12997^1, 96294.248             
                                                                     5

115, 4, 2, 13224, 2, 1, mp_115^4-115^2=13224^2+13224^1, 1.31518635 10              
                                                                     5

115, 4, 2, 13226, 2, 1, pm_115^4+115^2=13226^2-13226^1, 1.31712700 10              
                                                                     5

116, 4, 2, 13455, 2, 1, mp_116^4-116^2=13455^2+13455^1, 1.67836833 10              
                                                                     5

116, 4, 2, 13457, 2, 1, pm_116^4+116^2=13457^2-13457^1, 1.68054802 10              
                                                                     5

117, 4, 2, 13688, 2, 1, mp_117^4-117^2=13688^2+13688^1, 2.05041967 10              
                                                                     5

117, 4, 2, 13690, 2, 1, pm_117^4+117^2=13690^2-13690^1, 2.05212886 10              
                                                                  5

24, 6, 3, 13823, 2, 1, mp_24^6-24^3=13823^2+13823^1, 2.26818358 10              
                                                                  5

24, 6, 3, 13825, 2, 1, pm_24^6+24^3=13825^2-13825^1, 2.26976296 10              
                                                                     5

118, 4, 2, 13923, 2, 1, mp_118^4-118^2=13923^2+13923^1, 2.43062456 10              
                                                                     5

118, 4, 2, 13925, 2, 1, pm_118^4+118^2=13925^2-13925^1, 2.43249661 10              
                                                                     5

119, 4, 2, 14160, 2, 1, mp_119^4-119^2=14160^2+14160^1, 2.82243113 10              
                                                                     5

119, 4, 2, 14162, 2, 1, pm_119^4+119^2=14162^2-14162^1, 2.82447832 10              
                                                                     5

120, 4, 2, 14399, 2, 1, mp_120^4-120^2=14399^2+14399^1, 3.22370824 10              
                                                                     5

120, 4, 2, 14401, 2, 1, pm_120^4+120^2=14401^2-14401^1, 3.22607908 10              
Warning,  computation interrupted
> b;
                             14612             
> for b from 14612 to 25000 do
> if iperfpow(b) = FAIL then
> naive(b);
> fi;od;
 11, 8, 4, 14640, 2, 1, mp_11^8-11^4=14640^2+14640^1, 59848.205            
 11, 8, 4, 14642, 2, 1, pm_11^8+11^4=14642^2-14642^1, 60045.414            
                                                                     5

122, 4, 2, 14883, 2, 1, mp_122^4-122^2=14883^2+14883^1, 1.03239427 10             
                                                                     5

122, 4, 2, 14885, 2, 1, pm_122^4+122^2=14885^2-14885^1, 1.03421841 10             
                                                                     5

123, 4, 2, 15128, 2, 1, mp_123^4-123^2=15128^2+15128^1, 1.47488377 10             
                                                                     5

123, 4, 2, 15130, 2, 1, pm_123^4+123^2=15130^2-15130^1, 1.47674013 10             
                                                                     5

124, 4, 2, 15375, 2, 1, mp_124^4-124^2=15375^2+15375^1, 1.93530508 10             
                                                                     5

124, 4, 2, 15377, 2, 1, pm_124^4+124^2=15377^2-15377^1, 1.93725153 10             
                                                                 5

5, 12, 6, 15624, 2, 1, mp_5^12-5^6=15624^2+15624^1, 2.40085676 10             
                                                                 5

5, 12, 6, 15626, 2, 1, pm_5^12+5^6=15626^2-15626^1, 2.40325266 10             
                                                                     5

126, 4, 2, 15875, 2, 1, mp_126^4-126^2=15875^2+15875^1, 2.87859956 10             
                                                                     5

126, 4, 2, 15877, 2, 1, pm_126^4+126^2=15877^2-15877^1, 2.88059973 10             
                                                                     5

127, 4, 2, 16128, 2, 1, mp_127^4-127^2=16128^2+16128^1, 3.36806871 10             
                                                                     5

127, 4, 2, 16130, 2, 1, pm_127^4+127^2=16130^2-16130^1, 3.37020571 10             
                                                                   5

2, 28, 14, 16383, 2, 1, mp_2^28-2^14=16383^2+16383^1, 3.86934025 10             
                                                                   5

2, 28, 14, 16385, 2, 1, pm_2^28+2^14=16385^2-16385^1, 3.87124497 10             
                                                                     5

129, 4, 2, 16640, 2, 1, mp_129^4-129^2=16640^2+16640^1, 4.37167417 10             
                                                                     5

129, 4, 2, 16642, 2, 1, pm_129^4+129^2=16642^2-16642^1, 4.37395992 10             
                                                                 5

7, 10, 5, 16806, 2, 1, mp_7^10-7^5=16806^2+16806^1, 4.69765350 10             
                                                                 5

7, 10, 5, 16808, 2, 1, pm_7^10+7^5=16808^2-16808^1, 4.69950761 10             
                                                                     5

130, 4, 2, 16899, 2, 1, mp_130^4-130^2=16899^2+16899^1, 4.88131262 10             
                                                                     5

130, 4, 2, 16901, 2, 1, pm_130^4+130^2=16901^2-16901^1, 4.88358596 10             
Warning,  computation interrupted
> b;
                             16969            
> for b from 16969 to 30000 do
> if iperfpow(b) = FAIL then
> naive(b);
> fi;od;
131, 4, 2, 17160, 2, 1, mp_131^4-131^2=17160^2+17160^1, 48311.788          
131, 4, 2, 17162, 2, 1, pm_131^4+131^2=17162^2-17162^1, 48565.039          
                                                                     5

132, 4, 2, 17423, 2, 1, mp_132^4-132^2=17423^2+17423^1, 1.02007745 10           
                                                                     5

132, 4, 2, 17425, 2, 1, pm_132^4+132^2=17425^2-17425^1, 1.02237881 10           
                                                                  5

26, 6, 3, 17575, 2, 1, mp_26^6-26^3=17575^2+17575^1, 1.33314192 10           
                                                                  5

26, 6, 3, 17577, 2, 1, pm_26^6+26^3=17577^2-17577^1, 1.33543709 10           
                                                                     5

133, 4, 2, 17688, 2, 1, mp_133^4-133^2=17688^2+17688^1, 1.56726887 10           
                                                                     5

133, 4, 2, 17690, 2, 1, pm_133^4+133^2=17690^2-17690^1, 1.56981859 10           
                                                                     5

134, 4, 2, 17955, 2, 1, mp_134^4-134^2=17955^2+17955^1, 2.14730871 10           
                                                                     5

134, 4, 2, 17957, 2, 1, pm_134^4+134^2=17957^2-17957^1, 2.14996932 10           
Warning,  computation interrupted
> b;
                             18179          
> for b from 18179 to 30000 do
> if iperfpow(b) = FAIL then
> naive(b);
> fi;od;
135, 4, 2, 18224, 2, 1, mp_135^4-135^2=18224^2+18224^1, 9463.057         
135, 4, 2, 18226, 2, 1, pm_135^4+135^2=18226^2-18226^1, 9696.214         
136, 4, 2, 18495, 2, 1, mp_136^4-136^2=18495^2+18495^1, 67462.482         
136, 4, 2, 18497, 2, 1, pm_136^4+136^2=18497^2-18497^1, 67708.761         
                                                                     5

137, 4, 2, 18768, 2, 1, mp_137^4-137^2=18768^2+18768^1, 1.26790235 10          
                                                                     5

137, 4, 2, 18770, 2, 1, pm_137^4+137^2=18770^2-18770^1, 1.27042134 10          
                                                                     5

138, 4, 2, 19043, 2, 1, mp_138^4-138^2=19043^2+19043^1, 1.87450815 10          
                                                                     5

138, 4, 2, 19045, 2, 1, pm_138^4+138^2=19045^2-19045^1, 1.87663276 10          
                                                                     5

139, 4, 2, 19320, 2, 1, mp_139^4-139^2=19320^2+19320^1, 2.49465957 10          
                                                                     5

139, 4, 2, 19322, 2, 1, pm_139^4+139^2=19322^2-19322^1, 2.49752632 10          
                                                                     5

140, 4, 2, 19599, 2, 1, mp_140^4-140^2=19599^2+19599^1, 3.12829137 10          
                                                                     5

140, 4, 2, 19601, 2, 1, pm_140^4+140^2=19601^2-19601^1, 3.13083494 10          
Warning,  computation interrupted
> b;
                             19617         
> for b from 19617 to 30000 do
> if iperfpow(b) = FAIL then
> naive(b);
> fi;od;
 3, 18, 9, 19682, 2, 1, mp_3^18-3^9=19682^2+19682^1, 14794.180       
 3, 18, 9, 19684, 2, 1, pm_3^18+3^9=19684^2-19684^1, 15010.100       
141, 4, 2, 19880, 2, 1, mp_141^4-141^2=19880^2+19880^1, 60086.604       
141, 4, 2, 19882, 2, 1, pm_141^4+141^2=19882^2-19882^1, 60354.325       
                                                                     5

142, 4, 2, 20163, 2, 1, mp_142^4-142^2=20163^2+20163^1, 1.25822520 10        
                                                                     5

142, 4, 2, 20165, 2, 1, pm_142^4+142^2=20165^2-20165^1, 1.26082255 10        
                                                                     5

143, 4, 2, 20448, 2, 1, mp_143^4-143^2=20448^2+20448^1, 1.92700219 10        
                                                                     5

143, 4, 2, 20450, 2, 1, pm_143^4+143^2=20450^2-20450^1, 1.92987398 10        
                                                                  5

12, 8, 4, 20735, 2, 1, mp_12^8-12^4=20735^2+20735^1, 2.60625551 10        
                                                                  5

12, 8, 4, 20737, 2, 1, pm_12^8+12^4=20737^2-20737^1, 2.60938020 10        
                                                                     5

145, 4, 2, 21024, 2, 1, mp_145^4-145^2=21024^2+21024^1, 3.30136909 10        
                                                                     5

145, 4, 2, 21026, 2, 1, pm_145^4+145^2=21026^2-21026^1, 3.30401317 10        
                                                                     5

146, 4, 2, 21315, 2, 1, mp_146^4-146^2=21315^2+21315^1, 4.00988391 10        
                                                                     5

146, 4, 2, 21317, 2, 1, pm_146^4+146^2=21317^2-21317^1, 4.01260121 10        
Warning,  computation interrupted
> b;
                             21403       
> for b from 21403 to 30000 do
> if iperfpow(b) = FAIL then
> naive(b);
> fi;od;
147, 4, 2, 21608, 2, 1, mp_147^4-147^2=21608^2+21608^1, 50944.002      
147, 4, 2, 21610, 2, 1, pm_147^4+147^2=21610^2-21610^1, 51217.044      
                                                                     5

148, 4, 2, 21903, 2, 1, mp_148^4-148^2=21903^2+21903^1, 1.25061055 10       
                                                                     5

148, 4, 2, 21905, 2, 1, pm_148^4+148^2=21905^2-21905^1, 1.25325068 10       
                                                                  5

28, 6, 3, 21951, 2, 1, mp_28^6-28^3=21951^2+21951^1, 1.36991429 10       
                                                                  5

28, 6, 3, 21953, 2, 1, pm_28^6+28^3=21953^2-21953^1, 1.37259708 10       
                                                                     5

149, 4, 2, 22200, 2, 1, mp_149^4-149^2=22200^2+22200^1, 2.00318007 10       
                                                                     5

149, 4, 2, 22202, 2, 1, pm_149^4+149^2=22202^2-22202^1, 2.00609009 10       
                                                                     5

150, 4, 2, 22499, 2, 1, mp_150^4-150^2=22499^2+22499^1, 2.77370913 10       
                                                                     5

150, 4, 2, 22501, 2, 1, pm_150^4+150^2=22501^2-22501^1, 2.77626222 10       
                                                                     5

151, 4, 2, 22800, 2, 1, mp_151^4-151^2=22800^2+22800^1, 3.56150840 10       
                                                                     5

151, 4, 2, 22802, 2, 1, pm_151^4+151^2=22802^2-22802^1, 3.56454459 10       
Warning,  computation interrupted
> b;
                             22964      
> for b from 22964 to 30000 do
> if iperfpow(b) = FAIL then
> naive(b);
> fi;od;
152, 4, 2, 23103, 2, 1, mp_152^4-152^2=23103^2+23103^1, 37220.766     
152, 4, 2, 23105, 2, 1, pm_152^4+152^2=23105^2-23105^1, 37496.530     
                                                                     5

153, 4, 2, 23408, 2, 1, mp_153^4-153^2=23408^2+23408^1, 1.19365657 10      
                                                                     5

153, 4, 2, 23410, 2, 1, pm_153^4+153^2=23410^2-23410^1, 1.19719586 10      
Warning,  computation interrupted
> b;
                             23565     
> for b from 23565 to 30000 do
> if iperfpow(b) = FAIL then
> naive(b);
> fi;od;
154, 4, 2, 23715, 2, 1, mp_154^4-154^2=23715^2+23715^1, 40755.977   
154, 4, 2, 23717, 2, 1, pm_154^4+154^2=23717^2-23717^1, 41117.519   
                                                                     5

155, 4, 2, 24024, 2, 1, mp_155^4-155^2=24024^2+24024^1, 1.25692020 10    
                                                                     5

155, 4, 2, 24026, 2, 1, pm_155^4+155^2=24026^2-24026^1, 1.26088229 10    
                                                                     5

156, 4, 2, 24335, 2, 1, mp_156^4-156^2=24335^2+24335^1, 2.12385120 10    
                                                                     5

156, 4, 2, 24337, 2, 1, pm_156^4+156^2=24337^2-24337^1, 2.12692974 10    
                                                                  5

29, 6, 3, 24388, 2, 1, mp_29^6-29^3=24388^2+24388^1, 2.27037544 10    
                                                                  5

29, 6, 3, 24390, 2, 1, pm_29^6+29^3=24390^2-24390^1, 2.27342872 10    
                                                                     5

157, 4, 2, 24648, 2, 1, mp_157^4-157^2=24648^2+24648^1, 3.00361283 10    
                                                                     5

157, 4, 2, 24650, 2, 1, pm_157^4+157^2=24650^2-24650^1, 3.00669755 10    
Warning,  computation interrupted
> b;
                             24695   
> for b from 23565 to 40000 do
> if iperfpow(b) = FAIL then
> naive(b);
> fi;od;
154, 4, 2, 23715, 2, 1, mp_154^4-154^2=23715^2+23715^1, 40172.858  
154, 4, 2, 23717, 2, 1, pm_154^4+154^2=23717^2-23717^1, 40529.107  
                                                                     5

155, 4, 2, 24024, 2, 1, mp_155^4-155^2=24024^2+24024^1, 1.23991758 10   
                                                                     5

155, 4, 2, 24026, 2, 1, pm_155^4+155^2=24026^2-24026^1, 1.24382891 10   
                                                                     5

156, 4, 2, 24335, 2, 1, mp_156^4-156^2=24335^2+24335^1, 2.09451115 10   
                                                                     5

156, 4, 2, 24337, 2, 1, pm_156^4+156^2=24337^2-24337^1, 2.09754847 10   
                                                                  5

29, 6, 3, 24388, 2, 1, mp_29^6-29^3=24388^2+24388^1, 2.23891961 10   
                                                                  5

29, 6, 3, 24390, 2, 1, pm_29^6+29^3=24390^2-24390^1, 2.24193637 10   
                                                                     5

157, 4, 2, 24648, 2, 1, mp_157^4-157^2=24648^2+24648^1, 2.96219480 10   
                                                                     5

157, 4, 2, 24650, 2, 1, pm_157^4+157^2=24650^2-24650^1, 2.96523057 10   
Warning,  computation interrupted
> b;
                             24733  
> for b from 24733 to 40000 do
> if iperfpow(b) = FAIL then
> naive(b);
> fi;od;
158, 4, 2, 24963, 2, 1, mp_158^4-158^2=24963^2+24963^1, 64705.754 
158, 4, 2, 24965, 2, 1, pm_158^4+158^2=24965^2-24965^1, 64980.194 
Warning,  computation interrupted
> b;
                             25234 
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