# Ancillary Results About Polynomials

**Definition 1**

*Let and be polynomials. If and have no non-trivial common factor, then they are said to be coprime. That is, and are coprime if is a constant polynomial whenever and .*

**Theorem 1**(Euclid's algorithm)

*Let , be polynomials. Then there exist polynomials , with or such that*

Euclid's algorithm is really just long division. We are applying it
here to polynomials, where is the `quotient' and is the
`remainder'.

This is a corollary of Euclid's algorithm, and is equivalent to the definition of coprimality.

Gihan Marasingha 2005-09-19