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I am trying to prove that the $\gcd(a,b,c)$ = $\gcd(\gcd(a,b),c)$.

I think it has something to do with $\gcd$'s being able to be represented by a linear combination (that is $\gcd(a,b) = ax + by > 0$, for some integer $x$ and $y$).

Any help is appreciated!

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