Category:Definitions/Modulo Polynomial Division

This category contains definitions related to Modulo Polynomial Division.
Related results can be found in Category:Modulo Polynomial Division.

Let $\map f x$ and $\map g x$ be integral polynomials.

The operation of polynomial division modulo $m$ is defined as:

$\map f x \div_m \map g x$ equals the integral polynomial $\map h x$ such that:

$\map g x \times_m \map h x \equiv \map f x \pmod m$

where:

$m \in \Z$ is an integer

$\equiv$ means that the respective coefficients are congruent modulo $m$

provided such a polynomial exists.