1. ## Prime

Hi everybody

$(a,b)\in \mathbb{Z}^2$, p is prime number,

I must show that $p/(a^2+b^2)$ and $p/(a^2b^2)\Longrightarrow p/a$ and $p/b$

How to do it?

2. Originally Posted by lehder
Hi everybody

$(a,b)\in \mathbb{Z}^2$, p is prime number,

I must show that $p/(a^2+b^2)$ and $p/(a^2b^2)\Longrightarrow p/a$ and $p/b$

How to do it?
$p\mid a^2b^2\Longrightarrow p\mid a\,\,\,or\,\,\,p\mid b$ , since p is a prime. Suppose $p\mid a$ and thus also $p\mid a^2\Longrightarrow p\mid(a^2+b^2)-a^2\Longrightarrow p\mid b^2\Longrightarrow p\mid b$ as well.

Tonio