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Triangular Triangulation (Posted on 2014-08-30) Difficulty: 3 of 5
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.

No Solution Yet Submitted by K Sengupta    
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re: As many as you want. | Comment 3 of 4 |
(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 doesnít 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 canít
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

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