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Regional Olympiad - FBH 2010 Grade 9 Problem 4

Source: Regional Olympiad - Federation of Bosnia and Herzegovina 2010

September 27, 2018
tablecombinatorics

Problem Statement

In table of dimensions 2n×2n2n \times 2n there are positive integers not greater than 1010, such that numbers lying in unit squares with common vertex are coprime. Prove that there exist at least one number which occurs in table at least 2n23\frac{2n^2}{3} times