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

[Susanne Wienand]

Dear Alonso,

The equation in the proof on
https://oeis.org/wiki/Primes_as_differences_of_powers seems to be wrong.

If I plug in n = 12, a = 3, b = 4 and k = 5, I get for the left side:

(5^12 - 4^12) / (5^3 - 4^3) = 3727269

and for the rigth side:

5^9 - 4^9 = 1690981

Regards
Susanne


2013/9/13 Alonso Del Arte <alonso.delarte at gmail.com>

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