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# Def/Relatively prime

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Definition of Relatively prime: Suppose that $a,b \in \ZZ$. We say that $a$ and $b$ are relatively prime or coprime if the only common integer divisors of $a$ and $b$ are $1$ and $-1$. Equivalently, $a$ and $b$ are relatively prime if $GCD(a,b) = 1$.

More generally, suppose that $R$ is an integral domain, such as $\ZZ$ or $\RR[X]$, for example. We say that two elements $x,y$ of $R$ are relatively prime or coprime if the only common divisors of $x$ and $y$ are units in the ring $R$. In other words, if $r$ divides $x$ and $r$ divides $y$, then $r$ is a unit.

## Logical Connections

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

The following statements and definitions logically rely on the material of this page: State/Chinese remainder theorem, and State/Linear Diophantine equations can be solved with the Euclidean algorithm

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

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