[BB] For n ≥ 3, the greatest common divisor of n nonzero integers a1, a2, …, an can be def...

[BB] For n ≥ 3, the greatest common divisor of n nonzero integers a1, a2, …, an can be defined inductively by

Prove that gcd(a1, a2, …, an) is an integral linear combination of a1, a2, …, an for all n ≥ 2; that is, prove that there exist integers s1,…,sn such that gcd(a1, …, an) =s1, a1 + s2, a2,+ …, sn an