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Canada NT involving a bound

Source: 2019 ISL N7

September 22, 2020
number theoryIMO ShortlistIMO Shortlist 2019Additive Number Theory

Problem Statement

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