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Integers that can be expressed as ax+by

Source: Spain Mathematical Olympiad 2018 P5

March 17, 2018
number theorySpainDiophantine equation

Problem Statement

Let a,ba, b be coprime positive integers. A positive integer nn is said to be weak if there do not exist any nonnegative integers x,yx, y such that ax+by=nax+by=n. Prove that if nn is a weak integer and n<ab6n < \frac{ab}{6}, then there exists an integer k≥2k \geq 2 such that knkn is weak.
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