# Bézout’s Identity: iegcd igcdex

### 5.5.19 Bézout’s Identity: iegcd igcdex

Bézout’s Identity states that for any integers a and b, there exist integers u and v such that gcd(a,b) = au + bv. The iegcd command computes the coefficients u and v.
igcdex is a synonym for iegcd.

- iegcd takes two arguments:
  a and b, integers.
- iegcd(a,b) returns the list [u,v,d], where au+bv=d and d=gcd(a,b).

#### Example.

Input:

iegcd(48,30)

Output:

⎡ ⎣ | 2,−3,6 | ⎤ ⎦

In other words:

2 · 48+ (−3) · 30 =6