information:filtering
For three or more integers

Bézout's identity can be extended to more than two integers: if gcd (a 1, a 2, …, a n) = d {\displaystyle \gcd(a_{1},a_{2},\ldots,a_{n})=d} then there are integers x 1, x 2, …, x n {\displaystyle x_{1},x_{2},\ldots,x_{n}} such that d = a 1 x 1 + a 2 x 2 + ⋯ + a n x n {\displaystyle d=a_{1}x_{1}+a_{2}x_{2}+\cdots +a_{n}x_{n}} has the following properties: