IMO 2014 Shortlist N8
For every real number x, let }x} denote the distance between x and the nearest integer. Prove that for every pair pa,bq ...
Category: Number Theory
Problem
For every real number x, let }x} denote the distance between x and the nearest integer.
Prove that for every pair pa,bq of positive integers there exist an odd prime p and a positive
integer k satisfying ›
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a
pk
›
›
›
› › › › › b pk › › › ›
›
›
›
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a ` b
pk
›
›
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› “ 1.
(Hungary) 10 IMO 2014 South Africa