# ExtendedGCD Command

## CAS Syntax

ExtendedGCD( <Integer>,<Integer> )
Returns a list containing the integer coefficients s, t of Bézout's identity as+bt= GCD(a,b) and the greatest common divisor of the given integers a and b.
Results are calculated by applying the Extended Euclidean algorithm.
Example: ExtendedGCD(240,46) yields {-9,47,2}.
(Plugging the result into the Bézout's identity we have: -9 \cdot 240+47 \cdot 46=2).

ExtendedGCD( <Polynomial>, <Polynomial> )
Returns a list containing the polynomial coefficients S(x), T(x) of Bézout's identity for polynomials A(x)S(x) + B(x)T(x) = GCD(A(x), B(x)) and the greatest common divisor of the given polynomialsA(x) and B(x).
Results are calculated by applying the Extended Euclidean algorithm.
Example: ExtendedGCD(x^2-1,x+4) yields {1,-x+4,15}.
(Plugging the result into the Bézout's identity for polynomials we have: 1 \cdot (x^2-1) + (-x+4) \cdot (x+4) = 15).

Notes:
• The GCD of two polynomials is not unique (it's unique up to a scalar multiple).