A040162 - OEIS

%I #16 Sep 08 2022 08:44:53

%S 11,31,61,71,101,131,151,181,191,211,241,251,271,281,311,331,401,421,

%T 461,521,541,571,601,631,641,691,701,751,811,821,881,911,941,971,991,

%U 1031,1061,1151,1181,1201,1231,1291,1301,1321,1361,1381,1451,1481,1531

%N Primes p such that x^5 = 3 has no solution mod p.

%C Complement of A040161 relative to A000040. - _Vincenzo Librandi_, Sep 18 2012

%H Vincenzo Librandi, <a href="/A040162/b040162.txt">Table of n, a(n) for n = 1..1000</a>

%t ok[p_]:= Reduce[Mod[x^5 - 3, p] == 0, x, Integers] == False; Select[Prime[Range[300]], ok] (* _Vincenzo Librandi_, Sep 18 2012  *)

%o (Magma) [ p: p in PrimesUpTo(1600) | forall(t){x : x in ResidueClassRing(p) | x^5 ne 3} ]; // _Klaus Brockhaus_, Jun 03 2009

%o (Magma) [p: p in PrimesUpTo(1550) | not exists{x : x in ResidueClassRing(p) | x^5 eq 3} ]; // _Vincenzo Librandi_, Sep 18 2012

%Y Cf. A040161 (primes p such that x^5 = 3 has a solution mod p).

%K nonn,easy

%O 1,1

%A _N. J. A. Sloane_

%E More terms from _Klaus Brockhaus_, Jun 03 2009