When the integers a and b are coprime, the standard way of expressing this fact in mathematical notation is to indicate that their greatest common divisor is one, by the formula gcd(a, b) = 1 or (a, b) = 1. In their 1989 textbook See more

A set of integers $${\displaystyle S=\{a_{1},a_{2},\dots ,a_{n}\}}$$ can also be called coprime or setwise coprime if the greatest common … See more

Two ideals A and B in a commutative ring R are called coprime (or comaximal) if $${\displaystyle A+B=R.}$$ This generalizes See more

In machine design, an even, uniform gear wear is achieved by choosing the tooth counts of the two gears meshing together to be relatively … See more

The numbers 1 and −1 are the only integers coprime with every integer, and they are the only integers that are coprime with 0.
A number of conditions are equivalent to a and b being coprime:
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Given two randomly chosen integers a and b, it is reasonable to ask how likely it is that a and b are coprime. In this determination, it is … See more

This concept can be extended to other algebraic structures than $${\displaystyle \mathbb {Z} ;}$$ for example, polynomials whose See more