Question 86
$$
A_n = \{ (x, y) \in \mathbb{N} \times \mathbb{N} \mid \sqrt{x^2 + y + n} + \sqrt{y^2 + x + n} \in \mathbb{N} \}.
$$
Prove that for all $n \ge 1$, $A_n$ is a finite, nonempty set.
A_n = \{ (x, y) \in \mathbb{N} \times \mathbb{N} \mid \sqrt{x^2 + y + n} + \sqrt{y^2 + x + n} \in \mathbb{N} \}.
$$
Prove that for all $n \ge 1$, $A_n$ is a finite, nonempty set.