IMO 2023 Shortlist A6

Let k ě 2 be an integer. Determine all sequences of positive integers a1,a2,... for which there exists a monic polynomia...

IMO 2023 Shortlist A6

Category: Algebra

Problem

Let k ě 2 be an integer. Determine all sequences of positive integers a1,a2,... for which there exists a monic polynomial P of degree k with non-negative integer coefficients such that Ppanq “ an1an2 ¨¨¨an`k for every integer n ě 1. (Malaysia)