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

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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!