Question 118
Let $a$ and $b$ be positive integers such that $b-a$ is a prime. Prove that
$$(a^n + a + 1)(b^n + b + 1)$$
is not the square of an integer for infinitely many positive integers $n$.
$$(a^n + a + 1)(b^n + b + 1)$$
is not the square of an integer for infinitely many positive integers $n$.