But much of the beauty comes from the fact that all nontrivial solutions come from the trivial one! R. On Sun, 30 Apr 2006, Jpr2718@aol.com wrote:

David Wilson wrote:

...

Yes and the proof is surprisingly simple. Let x = 1, y = 0. Works for noninteger D as well.

Oops. Yes, of course. Thanks. I left out the word "nontrivial". Maybe I'll get it right this time:

For D > 0, D an integer, not a square, x^2 - Dy^2 = 1 has a solution in integers x, y, with y > 0.

John Robertson

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