Problem

Source: 2019 ISL N7

Tags: number theory, IMO Shortlist, IMO Shortlist 2019, Additive Number Theory



Prove that there is a constant $c>0$ and infinitely many positive integers $n$ with the following property: there are infinitely many positive integers that cannot be expressed as the sum of fewer than $cn\log(n)$ pairwise coprime $n$th powers. Canada