Divisibility-preserving function

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Template:Arithmetic function property

Definition

Suppose is an arithmetic function, i.e., is a function from the natural numbers to a commutative unital ring . We say that is divisibility-preserving if, whenever and are natural numbers such that divides , divides .

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

Relation with other properties

Stronger properties