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

Alonso Del Arte alonso.delarte at gmail.com
Thu Sep 12 05:22:53 CEST 2013


Lately, I've been working on a little simplification of several sequences
of 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

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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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