Take then you can check that . And on the other hand we have: which is a Pell's Equation. (And there are infinitely many solutions)

The minimal solution is and the solutions are generated by:

For example, the next is:

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- May 13th 2009, 11:08 AM #1

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## FLT Problem

Question:

Prove the following assertion: The system of simultaneous equations x^2+y^2=z^2-1 and x^2-y^2=w^2 has infinitely many solutions in positive integers x, y, z, w.

**I was thinking I could consider that for any integer n>=1****and then take x=2n^2 and y=2n, but I am not sure how that would work out.**

- May 14th 2009, 04:47 AM #2

- May 14th 2009, 10:21 AM #3

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