$\displaystyle (a,b)\in \mathbb{Z}^2$, p is prime number,
I must show that $\displaystyle p/(a^2+b^2)$ and $\displaystyle p/(a^2b^2)\Longrightarrow p/a $ and $\displaystyle p/b$
How to do it?
$\displaystyle p\mid a^2b^2\Longrightarrow p\mid a\,\,\,or\,\,\,p\mid b$ , since p is a prime. Suppose $\displaystyle p\mid a$ and thus also $\displaystyle p\mid a^2\Longrightarrow p\mid(a^2+b^2)-a^2\Longrightarrow p\mid b^2\Longrightarrow p\mid b$ as well.