A059337 Primes p such that x^35 = 2 has no solution mod p.

11, 29, 31, 41, 43, 61, 71, 101, 113, 127, 131, 181, 191, 197, 211, 239, 271, 281, 311, 331, 337, 379, 401, 421, 449, 461, 463, 491, 521, 541, 547, 601, 617, 631, 659, 661, 691, 701, 743, 751, 757, 761, 811, 821, 827, 881, 883, 911, 941, 967, 991, 1009, 1021

Offset

1,1

Comments

Complement of A049567 relative to A000040.

All members are 1 mod 5 or 1 mod 7, but not all such primes are members. 2731 is the first example of a prime in these residue classes with a solution. - Charles R Greathouse IV, Sep 21 2012

Links

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

Mathematica

ok[p_] := Reduce[Mod[x^35 - 2, p] == 0, x, Integers] == False; Select[Prime[Range[200]], ok ] (* Vincenzo Librandi, Sep 20 2012  *)

Prog

(Magma) [p: p in PrimesUpTo(1050) | not exists{x : x in ResidueClassRing(p) | x^35 eq 2 }]; // Vincenzo Librandi, Sep 20 2012
(PARI)
N=10^4;  default(primelimit, N);
ok(p, r, k)={ return ( (p==r) || (Mod(r, p)^((p-1)/gcd(k, p-1))==1) ); }
forprime(p=2, N, if (! ok(p, 2, 35), print1(p, ", ")));
/* Joerg Arndt, Sep 21 2012 */

Crossrefs

A000040, A049567.

Sequence in context: A196360 A072711 A005110 * A126240 A124110 A153768

Adjacent sequences: A059334 A059335 A059336 * A059338 A059339 A059340

Keyword

nonn,easy

Author

Klaus Brockhaus, Jan 26 2001

Status

approved