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A059337
Primes p such that x^35 = 2 has no solution mod p.
2
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
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
KEYWORD
nonn,easy
AUTHOR
Klaus Brockhaus, Jan 26 2001
STATUS
approved