Bezout's Identity

Jul 17, 2023

• Bézout’s identity - Wikipedia
• ramanujan.math.trinity.edu/rdaileda/teach/s20/m3326/lectures/bezout_handout.pdf

Bézout’s identity — Let a and b be  integers with  greatest common divisor d. Then there exist integers x and y such that ax + by = d. Moreover, the integers of the form az + bt are exactly the multiples of d.
Here the greatest common divisor of 0 and 0 is taken to be 0. The integers x and y are called Bézout coefficients for (a, b); they are not unique. A pair of Bézout coefficients can be computed by the  extended Euclidean algorithm

Let d = gcd(a, b). We will show that:

1. $d|m$;
2. m is a common divisor of a and b.