[seqfan] Re: A260119; Least positive integer k such that 2^n-1 and k^n-1 are relatively prime.

israel at math.ubc.ca israel at math.ubc.ca
Wed Sep 2 05:51:09 CEST 2015


If p is an odd prime such that p-1 divides n, then k^n - 1 is divisible by 
p for every k coprime to p, and in particular for k=2. Thus a(n) must be 
divisible by all such p. So for example, a(72) is divisible by 3, 5, 7, 13, 
19, 37, 73.

Cheers,
Robert

On Sep 1 2015, David Corneth wrote:

>So I've put a conjecture that might help finding such values of k, but I
>don't see a proof and I guess a faster program could be found. There are
>some examples to it, but I don't know what characteristic these n have. The
>conjecture is in the history of the sequence, see
>https://oeis.org/history/view?seq=A260119&v=36
>
> Any ideas on how to proceed?
>
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