Prove that there are infinitely many ordered triples of positive integers such that and is a perfect square.

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- October 19th 2008, 06:29 PMalexmahonePerfect square
Prove that there are infinitely many ordered triples of positive integers such that and is a perfect square.

- October 19th 2008, 09:05 PMNonCommAlg
put then you only need to find infinitely many such that for some the equation is known as Pell equation. it obviously has a solution

the general solution for is known to be:

__Note__: it's a good exercise to prove directly, without using what is known about Pell equation, that for all and also that is a perfect square.