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# Def/Divides

Definition of Divides: If $x$ and $y$ are integers, we say that $x$ divides $y$ if there exists an integer $m$ such that $y = mx$.

More generally, one often uses the word "divides" in the context of any commutative ring $R$. In this generality, the sentence "$x$ divides $y$", for two elements $x,y \in R$, means that: $$\exists m \in R, \mbox{ such that } y = xm.$$

The following are equivalent ways of stating that $x$ divides $y$:

## Logical Connections

This definition logically relies on the following definitions and statements: Def/Integer

To visualize the logical connections between this definition and other items of mathematical knowledge, you can visit any of the following clusters, and click the "Visualize" tab: Clust/Basic number theory, Clust/Basic ring theory