"Let p be a prime such that there exists a solution to the congruence [tex]x^2\equiv - 2\mod p[/tex].(adsbygoogle = window.adsbygoogle || []).push({});

THEN there are integers a and b such that [tex]a^2 + 2b^2 = p[/tex] or [tex]a^2 + 2b^2 = 2p[/tex]."

============================

I don't see why this is true. How can we prove this using basic concepts?

We know that there exists some integer x such that p|(x^{2}-2), what's next?

Any help is appreciated!

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Prime & Congruences

**Physics Forums | Science Articles, Homework Help, Discussion**