Difference between revisions of "Modular inverse"
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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>. | 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>. | ||
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Latest revision as of 17:17, 26 June 2025
In modular arithmetic, given a positive integer 
and an integer 
, we say that 
is the modular inverse of if 
. The inverse of is commonly denoted 
, and exists if and only if is relatively prime to .
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