Question 3
Find all positive integers $a$ and $b$ such that
$$
\frac{a^{2}+b}{b^{2}-a} \text{ and } \frac{b^{2}+a}{a^{2}-b}
$$
are both integers.
$$
\frac{a^{2}+b}{b^{2}-a} \text{ and } \frac{b^{2}+a}{a^{2}-b}
$$
are both integers.
MathNet 2002 — Part 01 Question 3
Math Olympiad Vault · MathNet 2002 — Part 01