A252279 Primes p congruent to 1 mod 16 such that x^8 = 2 has a solution mod p.

257, 337, 881, 1217, 1249, 1553, 1777, 2113, 2593, 2657, 2833, 4049, 4177, 4273, 4481, 4513, 4721, 4993, 5297, 6353, 6449, 6481, 6529, 6689, 7121, 7489, 8081, 8609, 9137, 9281, 9649, 10177, 10337, 10369, 10433, 10657, 11329, 11617, 11633, 12049, 12241, 12577

Offset

1,1

Comments

For a prime p congruent to 1 mod 16, the number 2 is an octavic residue mod p if and only if there are integers x and y such that x^2 + 256*y^2 = p.

Links

Arkadiusz Wesolowski, Table of n, a(n) for n = 1..10000

Index entries for related sequences

Prog

(Magma) [p: p in PrimesUpTo(12577) | p mod 16 eq 1 and exists(t){x : x in ResidueClassRing(p) | x^8 eq 2}]; // Arkadiusz Wesolowski, Dec 19 2020
(PARI) isok(p) = isprime(p) && (Mod(p, 16) == 1) && ispower(Mod(2, p), 8); \\ Michel Marcus, Dec 19 2020

Crossrefs

Subsequence of A045315.

Sequence in context: A062382 A289560 A256776 * A105345 A060261 A264348

Adjacent sequences: A252276 A252277 A252278 * A252280 A252281 A252282

Keyword

nonn

Author

Arkadiusz Wesolowski, Dec 16 2014

Status

approved