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{n\sqrt6 } > 1/n and {n\sqrt6 }> / 1/ (n-1/(5n)) , for odd n

Source: 2014 Belarus TST 8.2

December 29, 2020
algebrainequalities

Problem Statement

Prove that for all even positive integers nn the following inequality holds a) {n6}>1n\{n\sqrt6\} > \frac{1}{n} b){n6}>1n−1/(5n) \{n\sqrt6\}> \frac{1}{n-1/(5n)}
(I. Voronovich)
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