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...
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)