Define T(N) as the Nth triangular number.

Each of X and Y is a positive integer such that:
Each of T(X)+T(Y) and X+Y is a triangular number.

Does there exist an infinite number of pairs (X,Y) that satisfy the given conditions? Give reasons for your answer.

(In reply to As many as you want. by broll)

Broll. I agree that your equation [2] follows from the two original
conditions, so any solution of the problem will also satisfy equation [2];
for example {a, b, c, d} = {15, 21, 26, 8}. But it doesn’t follow that
all solutions of [2] will satisfy the original conditions;
for example {a, b, c, d} = {1, 5, 1, 2}.

I also agree that [2] has an infinite number of solutions, but I can’t
yet see any firm evidence that an infinite number of those solutions will
meet the original conditions. Am I missing something?

Posted by Harry on 2014-09-01 22:14:14