http://sites.google.com/site/asdfasdf23135/nt5.JPG

I know x^2 ≡ -2 (mod p) means that p|(x^2 -2), but I can't figure out how to continue with this.

Any help is appreciated!

[also under discussion in math links forum]

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- Feb 21st 2010, 03:19 AMkingwinnerPrime & Congruences
http://sites.google.com/site/asdfasdf23135/nt5.JPG

I know x^2 ≡ -2 (mod p) means that p|(x^2 -2), but I can't figure out how to continue with this.

Any help is appreciated!

[also under discussion in math links forum] - Feb 22nd 2010, 12:35 AMNonCommAlg
by Dirichlet's approximation theorem there exist integers and such that which gives us

now put and and show that and - Feb 22nd 2010, 03:57 AMkingwinner