Prove that a prime $p$ is expressible in the form $x^2+3y^2;x,y\in Z$ if and only if it is expressible in the form $ m^2+mn+n^2;m,n \in Z$.Can $p$ be replaced by a natural number $n$?
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Tags: number theory unsolved, number theory
Prove that a prime $p$ is expressible in the form $x^2+3y^2;x,y\in Z$ if and only if it is expressible in the form $ m^2+mn+n^2;m,n \in Z$.Can $p$ be replaced by a natural number $n$?