Problem

Source: ELMO SL 2018 N1

Tags: number theory, algebra, polynomial, induction



Determine all nonempty finite sets of positive integers $\{a_1, \dots, a_n\}$ such that $a_1 \cdots a_n$ divides $(x + a_1) \cdots (x + a_n)$ for every positive integer $x$. Proposed by Ankan Bhattacharya