IMO 2024 Shortlist N3

Determine all sequences a1, a2, ... of positive integers such that, for any pair of positive integers m ď n, the arithme...

IMO 2024 Shortlist N3

Category: Number Theory

Problem

Determine all sequences a1, a2, ... of positive integers such that, for any pair of positive integers m ď n, the arithmetic and geometric means am am1 ¨¨¨ an n ´ m 1 and pamam1 ¨¨¨anq n´m`1 are both integers. (Singapore)