Difference between revisions of "Mutually-prime numbers"
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''coprimes, relatively-prime numbers'' | ''coprimes, relatively-prime numbers'' | ||
| − | Integers without common (prime) divisors. The [[ | + | 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 [[ | + | The concept of being coprime may also be applied to polynomials and, more generally, to elements of a [[Euclidean ring]]. |
====Comments==== | ====Comments==== | ||
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====References==== | ====References==== | ||
<table><TR><TD valign="top">[a1]</TD> <TD valign="top"> I.M. Vinogradov, "Elements of number theory" , Dover, reprint (1954) (Translated from Russian)</TD></TR></table> | <table><TR><TD valign="top">[a1]</TD> <TD valign="top"> I.M. Vinogradov, "Elements of number theory" , Dover, reprint (1954) (Translated from Russian)</TD></TR></table> | ||
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Latest revision as of 18:57, 18 October 2014
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=12368
Mutually-prime numbers. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Mutually-prime_numbers&oldid=12368