Mutually-prime numbers
From Encyclopedia of Mathematics
The printable version is no longer supported and may have rendering errors. Please update your browser bookmarks and please use the default browser print function instead.
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.
Comments
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://encyclopediaofmath.org/index.php?title=Mutually-prime_numbers&oldid=33850
Mutually-prime numbers. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Mutually-prime_numbers&oldid=33850