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

[Alonso Del Arte]

Thank you very much, Robert, Eric, Vladimir.

I don't intend to add a comment to that effect to almost a hundred entries
in the OEIS, but I have added it to this OEIS Wiki page:
https://oeis.org/wiki/Primes_as_differences_of_powers


On Thu, Sep 12, 2013 at 5:05 AM, Vladimir Shevelev <shevelev at bgu.ac.il>wrote:

> 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>
> >
> > _______________________________________________
> >
> > Seqfan Mailing list - http://list.seqfan.eu/
> >
>
>  Shevelev Vladimir
>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/
>



-- 
Alonso del Arte
Author at SmashWords.com<https://www.smashwords.com/profile/view/AlonsoDelarte>
Musician at ReverbNation.com <http://www.reverbnation.com/alonsodelarte>