Difference between revisions of "Modular inverse"

 
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In Modular arithmetic, y is the modular inverse of x if:
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In [[modular arithmetic]], given a positive integer <math>m</math> and an integer <math>x</math>, we say that <math>y \in \{1,2,3,\ldots,m-1\}</math> is the modular inverse of <math>x</math> if <math>xy \equiv 1 \pmod{m}</math>. The inverse of <math>x</math> is commonly denoted <math>x^{-1}</math>, and exists if and only if <math>x</math> is relatively prime to <math>m</math>.
 
 
<cmath>xy \equiv 1 (\text{mod m})</cmath>
 
 
 
and if x is not relatively prime to m
 

Latest revision as of 03:05, 20 May 2024

In modular arithmetic, given a positive integer $m$ and an integer $x$, we say that $y \in \{1,2,3,\ldots,m-1\}$ is the modular inverse of $x$ if $xy \equiv 1 \pmod{m}$. The inverse of $x$ is commonly denoted $x^{-1}$, and exists if and only if $x$ is relatively prime to $m$.