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SMO 2022 Junior Round 2 Question 4

SMO · SMO 2022 Junior Round 2

Question 4

Let $n$ be a positive integer. Prove that $$n\sqrt{19}\{n\sqrt{19}\}>1,$$ where $\{x\}$ is the fractional part of the number $x$. (For example, $\{4.3\}=0.3$.)