# Mutually-prime numbers

coprimes, relatively-prime numbers

Integers without common (prime) divisors. The greatest common divisor of two coprimes $a$ and $b$ is 1, which is usually written as $(a,b)=1$. If $a$ and $b$ are coprime, there exist numbers $u$ and $v$, $|u|<|b|$, $|v|<|a|$, such that $au+bv=1$.

The concept of being coprime may also be applied to polynomials and, more generally, to elements of a Euclidean ring.

#### References

 [a1] I.M. Vinogradov, "Elements of number theory" , Dover, reprint (1954) (Translated from Russian)
How to Cite This Entry:
Mutually-prime numbers. Encyclopedia of Mathematics. URL: http://www.encyclopediaofmath.org/index.php?title=Mutually-prime_numbers&oldid=33850