2003 APMO 第 5 题

Given two positive integers $m$ and $n$, find the smallest positive integer $k$ such that among any $k$ people, either there are $2 m$ of them who form $m$ pairs of mutually acquainted people or there are $2 n$ of them forming $n$ pairs of mutually unacquainted people.

给定两个正整数$m$和$n$，找到最小的正整数$k$，使得在任何$k$个人中，要么有$2 m$组成$m$对相互熟悉的人，要么有$2 n$组成$n$对相互不认识的人。