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Silk Road 2021 P2

Source:

June 28, 2021
algebrainquality

Problem Statement

For every positive integer mm prove the inquality ∣{m}−12∣≥18(m+1)|\{\sqrt{m}\} - \frac{1}{2}| \geq \frac{1}{8(\sqrt m+1)} (The integer part [x][x] of the number xx is the largest integer not exceeding xx. The fractional part of the number xx is a number {x}\{x\} such that [x]+{x}=x[x]+\{x\}=x.)
A. Golovanov
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