Prove that $a^2  + b^2 + c^2 $ is not a prime number I am having difficulty solving this problem:
Let $a, b, c \in\mathbb{Z}$, $abc \neq 0$ and $a\neq c$ be such that
$$\frac{a}{c} = \frac{a^2+b^2}{c^2+b^2}.$$
Prove that $a^2 + b^2 + c^2$ is not a prime number.
Thanks in advance!

$\rm\  a^2+b^2+c^2 = (a+c)^2-b^2 + 2\: (b^2-ac)\ $ so $\rm\:b^2\! = ac\:\Rightarrow\:$ it factors (difference of squares)
