Bézout's Lemma

Bézout's Lemma (BL)

Lemma

For all integers and , there exist integers and such that , where

(See GCD)

Note that unlike the Euclidean Algorithm, we are not restricted to only positive integers, and we don't need

Examples

For and , we have , and and . (See GCD characterization theorem)

  1. For and , we haveWe also have and
  2. For and , we havWe also have ,