Prime numbers $\displaystyle x$ and $\displaystyle y$ are called twin primes, if $\displaystyle y = x + 2$. Prove that the numbers $\displaystyle x^4 + 4$ and $\displaystyle y^4 + 4$ are never relatively prime, if $\displaystyle x$ and $\displaystyle y$ are twin primes?

I'm not sure how to correctly approach this problem, but I've tried a few things and I think that $\displaystyle mod 4$ is involved somehow.

Please help, BG.