How to prove following statement :
Conjecture:
Odd prime $p$ is expressible as : $p=x^2+4\cdot y^2$ , $x,y > 0$
if and only if : $p\equiv 1 \pmod {12}$ or $p\equiv 5 \pmod {12}$ .
Similar statements (without a proof) related to the Fermat's theorem on sums of two squares can be found here .