Several of us claimed that if d=gcd(a,b,c) then d is a linear combination of a,b and c, i.e. that d=sa+tb+uc for some integers s,t, and u. That is true, but we only proved the analogous claim for the greatest common divisor of two numbers, i.e. when d=gcd(a,b). We need three.
The Attempt at a Solution
I know that gcd(a,b,c)=gcd(gcd(a,b)c). Can I use this to prove? If so, I'm not sure how.