A059637 Primes p such that x^45 = 2 has no solution mod p.

7, 11, 13, 19, 31, 37, 41, 61, 67, 71, 73, 79, 97, 101, 103, 109, 131, 139, 151, 163, 181, 191, 193, 199, 211, 241, 271, 281, 307, 311, 313, 331, 337, 349, 367, 373, 379, 401, 409, 421, 433, 461, 463, 487, 491, 521, 523, 541, 547, 571, 577, 601, 607, 613, 619

Offset

1,1

Comments

Complement of A049577 relative to A000040.

Links

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

Mathematica

ok[p_] := Reduce[Mod[x^45 - 2, p] == 0, x, Integers] == False; Select[Prime[Range[120]], ok] (* Vincenzo Librandi, Sep 21 2012 *)

Prog

(Magma) [p: p in PrimesUpTo(700) | not exists{x: x in ResidueClassRing(p) | x^45 eq 2}]; // Vincenzo Librandi, Sep 21 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, 45), print1(p, ", ")));
/* Joerg Arndt, Sep 21 2012 */

Crossrefs

Cf. A000040, A049577.

Sequence in context: A239710 A227921 A176620 * A059308 A075521 A084444

Adjacent sequences: A059634 A059635 A059636 * A059638 A059639 A059640

Keyword

nonn,easy

Author

Klaus Brockhaus, Feb 02 2001

Status

approved