For any integers `a` and `b`, there exist integers `s` and `t` such that `a``s` + `b``t` = gcd(`a`,`b`). The proof of this identity, as well as a method for finding `s` and `t`, is contained in the Extended Euclidean Algorithm. Bezout's Identity is useful for solving equations in modular rings (and, as a common special case, finding modular inverses) and solving Diophantine Equations.

Bezout's Identity is named for the 18th century French mathematician Etienne Bezout.