Problem

Source: 2024 CTST P4

Tags: number theory, 2024 CTST, China TST



Let $n$ be a positive square free integer, $S$ is a subset of $[n]:=\{1,2,\ldots ,n\}$ such that $|S|\ge n/2.$ Prove that there exists three elements $a,b,c\in S$ (can be same), satisfy $ab\equiv c\pmod n.$ Created by Zhenhua Qu