Question 76
Let $n \ge 2$ be a natural number and let $a_1, a_2, \dots, a_n$ be nonzero integers such that $a_1 + a_2 + \dots + a_n = a_1 a_2 \dots a_n$.
Prove that the number $(a_1^2 - 1)(a_2^2 - 1)\dots(a_n^2 - 1)$ is a perfect square.
Prove that the number $(a_1^2 - 1)(a_2^2 - 1)\dots(a_n^2 - 1)$ is a perfect square.