(a) prove that gcd(a,b,c) = gcd(a,gcd(b,c))

(b) a,b,c $\displaystyle \in $ N, with gcd(a,b) = gcd(a,c) = gcd(b,c). prove that gcd(a,b,c) = 1

(c) find a,b,c $\displaystyle \in $ N with gcd(a,b,c) = 1 but gcd(a,b), gcd(a,c), gcd(b,c) all > 1

i thought i would put them all in the same thread seeing as they may relate to each other (Nod)