[seqfan] Re: Prove that these exponents are primes (e.g., A062608)

[Vladimir Shevelev]

If n is not prime, e.g., n=p*q , p>1 is prime, then 42^(p*q) - 41^(p*q)  is multiple of 42^p - 41^p.

Regards,
Vladimir

----- Original Message -----
From: Alonso Del Arte <alonso.delarte at gmail.com>
Date: Wednesday, September 11, 2013 15:23
Subject: [seqfan] Prove that these exponents are primes (e.g., A062608)
To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>

> Lately, I've been working on a little simplification of several 
> sequencesof numbers such that k^n - (k - 1)^n is prime. A few of 
> these entries
> contain a remark to the effect that "all terms are prime," but 
> this is
> stated without proof. The most famous case is of course that of the
> exponents for the Mersenne primes, k = 2. The proof that the 
> primality of n
> is a necessary but not sufficient condition is well-known and 
> simple enough.
> 
> It seems simple to extend this to all k, but the proof has 
> eluded me. First
> I thought it would be a simple application of Fermat's little 
> theorem. Then
> I thought it was just a matter of generalizing the proof for k = 
> 2. Any
> thoughts?
> 
> Al
> 
> -- 
> Alonso del Arte
> Author at 
> SmashWords.com<https://www.smashwords.com/profile/view/AlonsoDelarte>Musician at ReverbNation.com <http://www.reverbnation.com/alonsodelarte>
> 
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> 

 Shevelev Vladimir‎