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A059349
Primes p such that x^32 = 2 has no solution mod p.
5
3, 5, 11, 13, 17, 19, 29, 37, 41, 43, 53, 59, 61, 67, 83, 97, 101, 107, 109, 113, 131, 137, 139, 149, 157, 163, 173, 179, 181, 193, 197, 211, 227, 229, 241, 251, 257, 269, 277, 281, 283, 293, 307, 313, 317, 331, 347, 349, 353, 373, 379, 389, 397, 401, 409, 419
OFFSET
1,1
COMMENTS
Complement of A049564 relative to A000040.
Differs from A014662 first at p=6529, then at p=21569. [R. J. Mathar, Oct 05 2008]
Differs from A045316 (x^8 == 2 (mod p) has no solution) first at a(37) = 257 which is not a term of A045316. See A070184 for all such terms. - M. F. Hasler, Jun 21 2024
LINKS
MATHEMATICA
ok[p_] := Reduce[Mod[x^32 - 2, p] == 0, x, Integers] == False; Select[Prime[Range[100]], ok ] (* Vincenzo Librandi, Sep 20 2012 *)
PROG
(Magma) [p: p in PrimesUpTo(450) | not exists{x : x in ResidueClassRing(p) | x^32 eq 2 }]; // Vincenzo Librandi, Sep 20 2012
CROSSREFS
Cf. A070184 = (this sequence) \ A045316.
Sequence in context: A045403 A059641 A014662 * A045316 A040100 A076757
KEYWORD
nonn,easy
AUTHOR
Klaus Brockhaus, Jan 27 2001
STATUS
approved