IMO 2023 Shortlist N5
Let a1 ă a2 ă a3 ă ¨¨¨ be positive integers such that ak1 divides 2pa1 a2 ¨¨¨ akq for every k ě 1. Suppose that for infi...
Category: Number Theory
Problem
Let a1 ă a2 ă a3 ă ¨¨¨ be positive integers such that ak1 divides 2pa1 a2 ¨¨¨ akq
for every k ě 1. Suppose that for infinitely many primes p, there exists k such that p divides
ak. Prove that for every positive integer n, there exists k such that n divides ak.
(Netherlands)