Is there anyone who can help me where to start. I'm having a hard time to figure this problem out. Thanks
Show that if a, b, and m are integers such that m ≥ 2 and a ≡ b( mod m), then gcd(a,m) = gcd(b,m).
for some integer k.
Let . Since and , it follows from that and is thus a common divisor of and .
Let be any common divisor of and . With a similar argument, we have that . By definition, since is the greatest common divisor of and , we have that .
This means that any common divisor of and is less than . Can you conclude?