|
|
A059258
|
|
Primes p such that x^53 = 2 has no solution mod p.
|
|
3
|
|
|
107, 743, 1061, 1697, 2333, 2969, 3181, 3499, 3923, 4241, 4877, 5407, 6043, 6361, 6679, 6997, 7103, 7951, 8269, 8693, 9011, 9859, 10177, 10601, 11131, 12721, 13463, 13781, 14629, 14947, 15053, 15583, 15901, 16007, 17491, 17597, 18127, 18233
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
Not so. The smallest counterexample is the prime 91373: 91373 == 1 (mod 53), but 2246^53 == 2 (mod 91373), therefore this prime is not in the sequence. - Bruno Berselli, Sep 20 2012
|
|
LINKS
|
|
|
MATHEMATICA
|
ok[p_] := Reduce[Mod[x^53 - 2, p] == 0, x, Integers] == False; Select[Prime[Range[2500]], ok] (* Vincenzo Librandi, Sep 20 2012 *)
|
|
PROG
|
(Magma) [p: p in PrimesUpTo(20000) | not exists{x: x in ResidueClassRing(p) | x^53 eq 2}]; // Vincenzo Librandi, Sep 20 2012
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|