I need help with this problem: Let $n,a_1,a_2,\ldots,a_n$ be integers such that $a_1a_2a_3\cdots a_n =n$ and $a_1+a_2+a_3+\cdots+a_n=0$. Prove that 4 divides n
I know that $a_i$ divides $n$ for any $i=1,2,3,\ldots,n$ and that $n>0$. So, there must be pair number of negative integers, but I don't know how to start the proof. I'm new at number theory. Need help please