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

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

For $a$, $k$, $n$ positive integers find $\gcd(a^n+1,a^k+1)$.
james_bond

Posts: 2
Joined: Sun May 17, 2009 4:06 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....

stapel_eliz

Posts: 1715
Joined: Mon Dec 08, 2008 4:22 pm

### Re:

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

Martingale

Posts: 350
Joined: Mon Mar 30, 2009 1:30 pm
Location: USA