Question 167
Let $a$, $b$, $c$ be positive integers and let $P_N = (a^2 + N)(b^2 + N)(c^2 + N)$ for any integer $N$. Show that
(1) there is a positive integer $N$ so that $P_N$ is not a perfect square,
(2) there is a positive integer $N$ so that $P_N$ is a perfect square.
(1) there is a positive integer $N$ so that $P_N$ is not a perfect square,
(2) there is a positive integer $N$ so that $P_N$ is a perfect square.