Problem

Source: 2016 IMO Shortlist A5

Tags: IMO Shortlist, algebra, Fractions, Hi



Consider fractions ab where a and b are positive integers. (a) Prove that for every positive integer n, there exists such a fraction ab such that nabn+1 and bn+1. (b) Show that there are infinitely many positive integers n such that no such fraction ab satisfies nabn+1 and bn.