Problems & Puzzles: Puzzles Puzzle 187. Triangles and Triangular numbers A certain Russian man called 'Eduardo' sent the following two puzzling tasks to Leonid Durman who  in his turn  shared with me these questions. As a matter of fact both questions seems to be a kind of apart from the primes, but they are strongly charming, indeed, to avoid momentarily this requirement. First two definitions:
The puzzling questions rescued by 'Eduardo' are:
The only known solution is A=8778, B=10296 & C=13530 (found by K. Zarankiewicz, according to L. Durman)
The only known solution is A = 14091, B = 3312 & C = 14475 (found by 'Eduardo', according to L. Durman) __________ Solution: Yves Gallot found a second solution to Task 2: A = 8013265, B = 3405996, C = 8707079 His algorithm is here:  for S a triangular even number Only two solutions for task 2 of puzzle 187 exist for P <= 43150*43151/2 (P <= 930,000,000). ***





