Competition problem — Number theory

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Number theory Difficulty 5.8 AIME, harder Prove it

9. $\sigma(n)$ is odd if and only if $n=k^{2}$ or $2 k^{2}$ .

Solution

9. Use equation (7).

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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.