Vipul: Created page with '{{arithmetic function property}} ==Definition== Suppose $f$ is an arithmetic function, i.e., $f$ is a function from the natural numbers to a [[com...'

2009-04-29T01:57:03Z

Created page with '{{arithmetic function property}} ==Definition== Suppose <math>f</math> is an arithmetic function, i.e., <math>f</math> is a function from the natural numbers to a [[com...'

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{{arithmetic function property}}

==Definition==

Suppose <math>f</math> is an [[arithmetic function]], i.e., <math>f</math> is a function from the [[natural number]]s to a [[commutative unital ring]] <math>R</math>. We say that <math>f</math> is divisibility-preserving if, whenever <math>d</math> and <math>n</math> are natural numbers such that <math>d</math> divides <math>n</math>, <math>f(d)</math> divides <math>f(n)</math>.

Note that whether a function is divisibility-preserving depends on what we consider the target ring.

==Relation with other properties==

===Stronger properties===

* [[Weaker than::Completely multiplicative function]]

Divisibility-preserving function - Revision history

Vipul: Created page with '{{arithmetic function property}} ==Definition== Suppose f is an arithmetic function, i.e., f is a function from the natural numbers to a [[com...'

Vipul: Created page with '{{arithmetic function property}} ==Definition== Suppose $f$ is an arithmetic function, i.e., $f$ is a function from the natural numbers to a [[com...'