Definition:Modulo Polynomial Division/Divisor
< Definition:Modulo Polynomial Division(Redirected from Definition:Polynomial Divisor Modulo Integer)
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Definition
Let $\map f x$ and $\map g x$ be integral polynomials.
Let $\map f x \div_m \map g x$ denote the operation of polynomial division modulo $m$:
- $\map f x \div_m \map g x$ equals the integral polynomial $\map h x$ such that:
- $\map g x \times_m \map h x \equiv \map f x \pmod m$
The polynomials $\map g x$ and $\map h x$ are (polynomial) divisors of $\map f x$ modulo $m$.
Examples
Arbitrary Example
Let $\map f x$ be the polynomial:
- $\map f x = 2 x^4 - 4 x - 3$
Then $\map f x$ has the following (polynomial) divisors modulo $7$:
- $2 x^2 + 3 x + 3$
- $x - 2$
- $x + 4$
Also known as
A polynomial divisor modulo $m$ is also known as a polynomial factor modulo $m$.
Also see
- Results about polynomial 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 $n$