Competition problem — Number theory

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Number theory Difficulty 5.5 AIME, harder Prove it

21. Prove: When $n>1$ , $1+1 / 2+\cdots+1 / n$ is not an integer.

Solution

21. Using the result of problem 20 ( $(\mathrm{i}$ ), find an integer such that its product with the sum $1+1 / 2+\cdots+1 / n$ is not an integer.

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Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic and difficulty added by this site.