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Old 2012-10-27, 18:28   #3
science_man_88
 
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"Forget I exist"
Jul 2009
Dumbassville

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Quote:
Originally Posted by Unregistered View Post
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.
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