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Added definition in logic notation & further explanation for f(1) = 1 condition. |
Adding local short description: "Arithmetic function", overriding Wikidata description "arithmetic function that is multiplicative for every pair of integers, not necessarily coprime" |
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{{Short description|Arithmetic function}}
In [[number theory]], functions of [[positive integer]]s which respect products are important and are called '''completely multiplicative functions''' or '''totally multiplicative functions'''. A weaker condition is also important, respecting only products of [[coprime]] numbers, and such functions are called [[multiplicative function]]s. Outside of number theory, the term "multiplicative function" is often taken to be synonymous with "completely multiplicative function" as defined in this article.
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