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...
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)