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Let $x, y \in \Z$.
Then $x$ is an associate of $y$ if and only if they are both divisors of each other.
That is, $x$ and $y$ are associates if and only if $x \divides y$ and $y \divides x$.
Also known as
The statement $x$ is an associate of $y$ can be expressed as $x$ is associated to $y$.
- 1982: P.M. Cohn: Algebra Volume 1 (2nd ed.) ... (previous) ... (next): Chapter $2$: Integers and natural numbers: $\S 2.2$: Divisibility and factorization in $\mathbf Z$