Prove that there are infinitely many positive integers n such n(n+1) can b expressed as a sum of two positive squares in at least two different ways.(a^2 + b^2 and b^2 + a^2 are considered as the same representation.....

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- Sep 16th 2007, 09:50 AM #1

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- Sep 16th 2007, 10:16 AM #2

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- Sep 18th 2007, 07:41 AM #3

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- Sep 20th 2007, 07:38 PM #4

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If you find such an so that it is a square

**and**is a square. Then and are integers.

This means,

And,

.

So the question is. "Are there infinite many such having this property?". The answer is yes. This is a consequence of the Pellian equation is you really want to show it.

- Sep 22nd 2007, 07:18 AM #5

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