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BUILT-IN MATHEMATICA SYMBOL

PolynomialExtendedGCD

gives the extended GCD of

and

treated as univariate polynomials in x.

PolynomialExtendedGCD[poly₁, poly₂, x, Modulus->p]
gives the extended GCD over the integers mod prime p.

Compute the extended GCD:

The second part gives coefficients of a linear combination of polynomials that yields the GCD:

Compute the extended GCD:

Out[2]=

The second part gives coefficients of a linear combination of polynomials that yields the GCD:

Out[3]=

Polynomials with numeric coefficients:

Polynomials with symbolic coefficients:

Relatively prime polynomials:

Extended GCD over the integers:

Extended GCD over the integers modulo 2:

Given polynomials

, and

, find polynomials

and

such that

A solution exists if and only if

is divisible by

The extended GCD of

and

, such that

and

up to a factor not containing

r and s are uniquely determined by the following Exponent conditions:

divides

and