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Difference between revisions of "Mutually-prime numbers"

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(Category:Number theory)
 
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''coprimes, relatively-prime numbers''
 
''coprimes, relatively-prime numbers''
  
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Integers without common (prime) divisors. The [[Greatest common divisor|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 $au+bv=1$.
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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 $au+bv=1$.
  
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The concept of being coprime may also be applied to polynomials and, more generally, to elements of a [[Euclidean ring|Euclidean ring]].
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The concept of being coprime may also be applied to polynomials and, more generally, to elements of a [[Euclidean ring]].
  
 
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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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[[Category:Number theory]]

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=33850
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