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

[israel at math.ubc.ca]

If n = ab, x^n - y^n = (x^a)^b - (y^a)^b is divisible by x^a - y^a.
Note that k^a - (k-1)^a > 1 for a > 1.

Cheers, 
Robert Israel


On Sep 11 2013, Alonso Del Arte wrote:

> 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
>
>