Competition problem — Number theory

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Number theory Difficulty 6.0 National olympiad Prove it

19. Use the Möbius inversion formula to show that if $f$ is an arithmetic function and $F$ is the arithmetic function defined by
$F(n)=\sum_{d \mid n} f(d)$
then if $F$ is multiplicative, so is $f$ .

Solution

None

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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.