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Triangular and Square Settlement (Posted on 2015-10-13) Difficulty: 3 of 5
A is a triangular number and B is a perfect square such that:
A – B = 2015

Find the four smallest values of A+B

No Solution Yet Submitted by K Sengupta    
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extended list | Comment 6 of 7 |
(In reply to re: possible solution. //infinitely many ? by Ady TZIDON)

Extending the check through the 10,000th triangular number yields ever more results. The 9680th triangular gives A+B=93710065.

                                   ordinal
       A          B        A+B     tri   sq
     2016         1        2017     63    1
     2211       196        2407     66   14
     2415       400        2815     69   20
     3240      1225        4465     80   35
     5151      3136        8287    101   56
     8256      6241       14497    128   79
    10296      8281       18577    143   91
    17391     15376       32767    186  124
    18915     16900       35815    194  130
    32640     30625       63265    255  175
    41616     39601       81217    288  199
    72771     70756      143527    381  266
   139656    137641      277297    528  371
   246051    244036      490087    701  494
   315615    313600      629215    794  560
   557040    555025     1112065   1055  745
   608856    606841     1215697   1103  779
  1075311   1073296     2148607   1466 1036
  1380291   1378276     2758567   1661 1174
  2438736   2436721     4875457   2208 1561
  4710915   4708900     9419815   3069 2170
  8325240   8323225    16648465   4080 2885
 10688376  10686361    21374737   4623 3269
 18889731  18887716    37777447   6146 4346
 20649951  20647936    41297887   6426 4544
 36495696  36493681    72989377   8543 6041
 46856040  46854025    93710065   9680 6845

  Posted by Charlie on 2015-10-14 08:09:55
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