# Thread: Another GCD problem

1. ## Another GCD problem

prove that gcd(((a^m)-1)/(a-1));(a-1))=((a-1);m)

Help would be really appreciated.

2. ## Re: Another GCD problem

Originally Posted by RuyHayabusa
prove that gcd(((a^m)-1)/(a-1));(a-1))=((a-1);m)

Help would be really appreciated.
Please show us what you've been able to do so far.

-Dan

3. ## Re: Another GCD problem

First prove then use the following

$\displaystyle a^m = 1 + \sum _{k=1}^m c_k (a-1)^k$

where the $\displaystyle c_k$ are integers

4. ## Re: Another GCD problem

I've finally solved it using Bezout's theorem.

5. ## Re: Another GCD problem

I would like to see a solution of this problem using Bezout's theorem.

Here is a reference to Bezout's theorem as seen in Wikipedia

Bézout's theorem - Wikipedia, the free encyclopedia

.....X and Y are two algebraic curves in the Euclidean plane whose implicit equations are polynomials of degrees m and n without any non-constant common factor, then the number of intersection points does not exceed mn.

Thanks