Problem

Source: ELMO 2020 P5

Tags: number theory, algebra, Polynomials



Let $m$ and $n$ be positive integers. Find the smallest positive integer $s$ for which there exists an $m \times n$ rectangular array of positive integers such that each row contains $n$ distinct consecutive integers in some order, each column contains $m$ distinct consecutive integers in some order, and each entry is less than or equal to $s$. Proposed by Ankan Bhattacharya.