|
|
A059223
|
|
Primes p such that x^37 = 2 has no solution mod p.
|
|
4
|
|
|
149, 223, 593, 1259, 1481, 1777, 1999, 2221, 2591, 2887, 3109, 3257, 3331, 3701, 3923, 4219, 4441, 4663, 5107, 5477, 6143, 6217, 6661, 6883, 7253, 7549, 7919, 7993, 8363, 8807, 9029, 9103, 9473, 9547, 9769, 10139, 10657, 11027, 12211, 12433
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
Not so. The smallest counterexample is 11471: 11471 == 1 (mod 37), but 43^37 == 2 (mod 11471), therefore this prime is not in the sequence. - Bruno Berselli, Sep 12 2012
|
|
LINKS
|
|
|
MATHEMATICA
|
Select[Prime[Range[PrimePi[12500]]], ! MemberQ[PowerMod[Range[#], 37, #], Mod[2, #]] &] (* T. D. Noe, Sep 12 2012 *)
ok[p_]:= Reduce[Mod[x^37 - 2, p] == 0, x, Integers] == False; Select[Prime[Range[2000]], ok] (* Vincenzo Librandi, Sep 19 2012 *)
|
|
PROG
|
(Magma) [p: p in PrimesUpTo(13000) | forall{x: x in ResidueClassRing(p) | x^37 ne 2}]; // Bruno Berselli, Sep 12 2012
(PARI)
N=10^5; 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, 37), print1(p, ", ")));
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|