[seqfan] Re: Two questions looking for answers
Don Reble
djr at nk.ca
Fri Oct 26 03:14:29 CEST 2018
> 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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