1. ## 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?"

2. 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 $a^{(m,n)}-1|a^m-1$ and $a^{(m,n)}-1|a^n-1$? Why can't any value greater than $a^(m,n)-1$ divide both of them?