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# Def/Invertible residue

Definition of Invertible residue: Suppose that $m$ is a positive integer. An invertible residue, modulo $m$, is a residue $\bar x$, modulo $m$, such that there exists a residue $\bar y$, modulo $m$, such that: $$\bar x \cdot \bar y = \bar 1, \mbox{ modulo } m.$$

A residue $\bar x$, modulo $m$, is an invertible residue if and only if $GCD(x,m) = 1$.

## Logical Connections

This definition logically relies on the following definitions and statements: Def/Residue

The following statements and definitions logically rely on the material of this page: Def/Totient, State/Computing the totient of a prime power, State/Fermat Euler theorem, State/Multiplicative inverses exist mod p, State/Products of invertible residues are invertible, and State/Relative primality to the modulus is equivalent to invertibility of a residue

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