[seqfan] Re: Two questions looking for answers

[Neil Sloane]

Don,  Thanks for solving that problem!  I added your answer to A320481.
Best regards
Neil



On Thu, Oct 25, 2018 at 9:18 PM Don Reble via SeqFan <seqfan at list.seqfan.eu>
wrote:

> > A045318 Primes p such that x^8 = 3 has no solution mod p.
> > A301916 Primes which divide numbers of the form 3^k + 1.
>
> > The terms in A301916 but not in A045318 are ... A320481.
> >     2, 769, 1297, 6529, 7057, 8017, 8737, 12097, 12289. ...
> > ...what are these primes?
>
>     Let POT(x) be the largest power of 2 which divides x.
>     The non-2 values are those primes P, such that
>         2 <= POT(the order of 3 modulo P) <= POT(P-1)/8.
>     "2 <=" so that P divides some 3^k+1,
>     "<= POT(P-1)/8" so that 3 has an eighth root modulo P.
>
>     POT = A006519; A062117 is the order of 3 modulo prime(n).
>
> --
> Don Reble  djr at nk.ca
>
>
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