1977 IMO 第 5 题

Let $a$ and $b$ be positive integers. When $a^2+b^2$ is divided by $a+b$, the quotient is $q$ and the remainder is $r$. Find all pairs $(a,b)$ such that $q^2+r=1977$.

设 $a$ 和 $b$ 为正整数。用 $a+b$ 除 $a^2+b^2$ 时，商为 $q$，余数为 $r$。求所有满足 $q^2+r=1977$ 的数对 $(a,b)$。