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Fractional part inequality

Source: Bosnia and Herzegovina TST 2006 day 1 problem 3

July 14, 2016
fractional partInequalitynumber theorypositive integerinequalities

Problem Statement

Prove that for every positive integer nn holds inequality {n7}>3714n\{n\sqrt{7}\}>\frac{3\sqrt{7}}{14n}, where {x}\{x\} is fractional part of xx.
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