Thread: GCD Proof

I'm not sure at all how to start in answering the following:

GCD (a^(m) - 1, a^(n) - 1) = a^GCD(m, n) - 1


Are there any other properties of GCD other than GCD (a, b) = GCD (a - b, b)?

djino
"What that even help?"

Originally Posted by djino

I'm not sure at all how to start in answering the following:

GCD (a^(m) - 1, a^(n) - 1) = a^GCD(m, n) - 1


Are there any other properties of GCD other than GCD (a, b) = GCD (a - b, b)?

djino
"What that even help?"

Does and ? Why can't any value greater than divide both of them?