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

Author

Arkadiusz Wesolowski, Dec 16 2014

Keywords

• nonn

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

Crossrefs

Subsequence of A045315.

Has A070184 as a subsequence.

Programs

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