# Abstract Algebra

1. Sep 21, 2010

### silvermane

1. The problem statement:
Consider 3 positive integers, a, b, c. Let $$d_{1}$$ = gcd(b,c) = 1. Prove that the greatest number dividing all three of a, b, c is gcd($$d_{1}$$,c)

3. My go at the proof and thoughts:

Well, I know that the common divisors of a and b are precisely the divisors of $$d_{1}$$

I also know that to get the gcd(a,b,c) we need to consider a,b's gcd with c to get the overall gcd for all three numbers.

I think that I need to write it as a linear combination for a,b, and c, but I'm stuck. This problem seems easy too, but I think there's something that I'm missing.