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A049587
Primes p such that x^55 = 2 has a solution mod p.
2
2, 3, 5, 7, 13, 17, 19, 29, 37, 43, 47, 53, 59, 73, 79, 83, 97, 103, 107, 109, 113, 127, 137, 139, 149, 151, 157, 163, 167, 173, 179, 193, 197, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 277, 283, 293, 307, 313, 317, 337, 347, 349, 359, 367, 373, 379
OFFSET
1,1
COMMENTS
Complement of A059642 relative to A000040. - Vincenzo Librandi, Sep 14 2012
MATHEMATICA
ok[p_] := Reduce[Mod[x^55 - 2, p] == 0, x, Integers] =!= False; Select[Prime[Range[100]], ok] (* Vincenzo Librandi, Sep 14 2012 *)
PROG
(Magma) [p: p in PrimesUpTo(400) | exists(t){x : x in ResidueClassRing(p) | x^55 eq 2}]; // Vincenzo Librandi, Sep 14 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, 55), print1(p, ", ")));
/* Joerg Arndt, Sep 21 2012 */
CROSSREFS
Sequence in context: A133244 A077040 A153503 * A293008 A038903 A136003
KEYWORD
nonn,easy
STATUS
approved