Thread: Generalized Mersenne Primes View Single Post
2012-10-27, 18:28   #3
science_man_88

"Forget I exist"
Jul 2009
Dumbassville

8,369 Posts

Quote:
 Originally Posted by Unregistered I believe that I remember a theorem having to do with Generalized Mersenne primes of the form: (a^n+b^n)/(a+b). The theorem states that if (a^n+b^n)/(a+b) is prime, then n must also be prime. Does anyone know a reference that has a proof of this? Thanks.
Code:
(15:18)>for(a=1,100,
for(b=a,100,
for(n=1,100,
if(((a^n+b^n)/(a+b))%1.==0 &&isprime((a^n+b^n)/(a+b)) && !isprime(n),
print(((a^n+b^n)/(a+b))","a","b","n);)
)
)
)
Quote:
 14321,6,26,4 280097,12,69,4 4481,14,18,4 134417,24,57,4
shows that n=4 has counterexamples.