A059349 Primes p such that x^32 = 2 has no solution mod p.

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

Author

Klaus Brockhaus, Jan 27 2001

Keywords

• nonn
• easy

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

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000040, A049564, A216747.

Cf. A070184 = (this sequence) \ A045316.

Programs

Magma

[p: p in PrimesUpTo(450) | not exists{x : x in ResidueClassRing(p) | x^32 eq 2 }]; // Vincenzo Librandi, Sep 20 2012

Mathematica

ok[p_] := Reduce[Mod[x^32 - 2, p] == 0, x, Integers] == False; Select[Prime[Range[100]], ok ] (* Vincenzo Librandi, Sep 20 2012  *)