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BxMo 2015, Problem 1

Source: Benelux Mathematical Olympiad 2015, Problem 1

May 10, 2015
algebra

Problem Statement

Determine the smallest positive integer qq with the following property: for every integer mm with 1⩽m⩽10061\leqslant m\leqslant 1006, there exists an integer nn such that m1007q<n<m+11008q\dfrac{m}{1007}q<n<\dfrac{m+1}{1008}q.
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