Prove Let a b n N Suppose that a Nb Then gcda n gcdb n Prov

Prove: Let a, b, n N. Suppose that a _Nb. Then gcd(a, n) = gcd(b, n). Prove: Let a, b, n N. If gcd(a, n) = gcd(b, n) = 1, then gcd(ab, n) = 1.

Solution

Given gcd(a,n)=1

so n is not a factor of a

gcd(b,n)=1

so n is not a factor of b

therefore n is not a factor of ab since n is not a facor of a,b

so gcd(ab,n)=1