Question

(a). Is it true that for all set of positive integers a, b, c. gcd(a,c) + gcd(b,c) = gcd(a + b,c). Explain

(b) Is it true that there exist a set of positive integers a,b,c, such that gcd(a,c) + gcd(b,c) = gcd(a + b,c). Explain

Answer 1

no. gcd(2,10)=2 gcd(5,10)=5 gcd(7,10)=1
yes gcd(2,12)=2 gcd(4,12)=4 gcd(6,12)=6