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

[Alonso Del Arte]

Oh yes, the exponent laws, I had forgotten about those. The proof follows
immediately. Thank you very much, Robert.

Al


On Thu, Sep 12, 2013 at 12:17 AM, <israel at math.ubc.ca> wrote:

> 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
>>
>>
>>
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Alonso del Arte
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