Category:Definitions/Residues (Number Theory)

This category contains definitions related to residues in the context of number theory.
Related results can be found in Category:Residues (Number Theory).

Let $m, n \in \N$ be natural numbers.

Let $a \in \Z$ be an integer such that $a$ is not divisible by $m$.

Then $a$ is a residue of $m$ of order $n$ if and only if:

$\exists x \in \Z: x^n \equiv a \pmod m$

where $\equiv$ denotes modulo congruence.