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

Help would be really appreciated.

Printable View

- Nov 17th 2013, 06:01 AMRuyHayabusaAnother GCD problem
prove that gcd(((a^m)-1)/(a-1));(a-1))=((a-1);m)

Help would be really appreciated. - Nov 17th 2013, 07:03 AMtopsquarkRe: Another GCD problem
- Nov 18th 2013, 06:00 AMIdeaRe: 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 - Nov 21st 2013, 04:44 AMRuyHayabusaRe: Another GCD problem
I've finally solved it using Bezout's theorem.

- Nov 22nd 2013, 07:27 AMIdeaRe: 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