login
A252279
Primes p congruent to 1 mod 16 such that x^8 = 2 has a solution mod p.
2
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.
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.
Has A070184 as a subsequence.
Sequence in context: A062382 A289560 A256776 * A105345 A060261 A264348
KEYWORD
nonn
AUTHOR
STATUS
approved