I'd really like your help with the following Number Theory question:
I need to show that if I can write an integer $n=x^2+3y^2$ so in the factorization of $n$ to primes, every $p \equiv 2\pmod 3$ would be with a even power, I mean if $n=\prod p^{a(p)}$ so $a(p)$ is even for all $p \equiv 2 \pmod 3$, where $p$ is prime.
I don't rally know how to start this one.
Thank you.