Modular inverse

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 $m$ .