1984 IMO 第 2 题

(CAN 2) Prove: (a) There are infinitely many triples of positive integers $m, n, p$ such that $4 m n-m-n=p^{2}-1$. (b) There are no positive integers $m, n, p$ such that $4 m n-m-n=p^{2}$.

(CAN 2) 证明： (a) 存在无穷多个正整数三元组 $m, n, p$，使得 $4 m n-m-n=p^{2}-1$。 (b) 不存在满足 $4 m n-m-n=p^{2}$ 的正整数 $m, n, p$。