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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.
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
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