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Definition: Multiplicative Functions

An arithmetic function $$\beta$$ with at least one $$m\in\mathbb N$$ with $$\beta(m)\neq 0$$ is called:

1. multiplicative, $$\beta(mn)=\beta(m)\beta(n)$$ for all relatively prime $$m,n\in\mathbb N$$,
2. completely multiplicative, if $$\beta(mn)=\beta(m)\beta(n)$$ for all $$m,n\in\mathbb N$$.

| | | | | created: 2014-03-06 17:30:59 | modified: 2019-04-06 07:16:08 | by: bookofproofs | references: [1272]

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