Greatest common divisor of (a^n + 1, a^k + 1) for ints a,k,n

Sequences, counting (including probability), logic and truth tables, algorithms, number theory, set theory, etc.
james_bond
Posts: 2
Joined: Sun May 17, 2009 4:06 pm
Contact:

Greatest common divisor of (a^n + 1, a^k + 1) for ints a,k,n

Postby james_bond » Sun May 17, 2009 4:18 pm

For , , positive integers find .

User avatar
stapel_eliz
Posts: 1737
Joined: Mon Dec 08, 2008 4:22 pm
Contact:

Postby stapel_eliz » Sun May 17, 2009 7:22 pm

I think the greatest common divisor will be 2 for odd values of "a", and 1 for even values of "a". But you probably need to prove this....

:popcorn:

User avatar
Martingale
Posts: 350
Joined: Mon Mar 30, 2009 1:30 pm
Location: USA
Contact:

Re:

Postby Martingale » Mon May 18, 2009 6:11 am

stapel_eliz wrote:I think the greatest common divisor will be 2 for odd values of "a", and 1 for even values of "a". But you probably need to prove this....


if a=5, n=7 and k=9..then the

gcd(5^7+1,5^9+1)=6


Return to “Discrete Math”