- #1
kingwinner
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"Let p be a prime such that there exists a solution to the congruence [tex]x^2\equiv - 2\mod p[/tex].
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|(x2 -2), what's next?
Any help is appreciated!
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|(x2 -2), what's next?
Any help is appreciated!