Difference between revisions of "Modular inverse"
Scrabbler94 (talk | contribs) |
|||
Line 1: | Line 1: | ||
− | In | + | 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>. |
− | |||
− | < | ||
− | |||
− | and if x is |
Latest revision as of 03:05, 20 May 2024
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 .