Definition:Modulo Division/Divisor
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Definition
Let $m \in \Z$ be an integer.
Let $\Z_m$ be the set of integers modulo $m$:
- $\Z_m = \set {0, 1, \ldots, m - 1}$
For all $a, b \in \Z_m$, let $a \div_m b$ denote the operation of division modulo $m$:
- $a \div_m b$ equals the integer $q \in \Z_m$ such that $b \times_m q \equiv a \pmod m$
The integers $b$ and $q$ are divisors of $a$ modulo $m$.
Examples
5 modulo 12
In modulo $12$ division, $5$ has the following divisors:
- $1, 5, 7, 11$
8 modulo 12
In modulo $12$ division, $8$ has the following divisors:
- $1, 2, 4, 5, 7, 8, 10, 11$
Also known as
A divisor modulo $m$ is also known as a factor modulo $m$.
Also see
- Results about divisors modulo $m$ can be found here.
Sources
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): factor modulo $n$
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): factor modulo $n$