cp's OEIS Frontend

A070180 Primes p such that x^3 = 2 has a solution mod p, but x^(3^2) = 2 has no solution mod p.

%I A070180 #11 Sep 08 2022 08:45:05
%S A070180 109,307,433,739,811,919,1423,1459,1999,2017,2143,2179,2251,2287,2341,
%T A070180 2791,2917,2953,3061,3259,3331,3457,3889,4177,4339,4519,4663,5113,
%U A070180 5167,5419,5437,5653,6301,6427,6661,6679,6967,7723,7741,8011,8389,8713
%N A070180 Primes p such that x^3 = 2 has a solution mod p, but x^(3^2) = 2 has no solution mod p.
%o A070180 (PARI) forprime(p=2,8800,x=0; while(x<p&&x^3%p!=2%p,x++); if(x<p,y=0; while(y<p&&y^(3^2)%p!=2%p,y++); if(y==p,print1(p,","))))
%o A070180 (Magma) [p: p in PrimesUpTo(10000) | not exists{x: x in ResidueClassRing(p) | x^9 eq 2} and exists{x: x in ResidueClassRing(p) | x^3 eq 2}]; // _Vincenzo Librandi_, Sep 21 2012
%o A070180 (PARI)
%o A070180 ok(p, r, k1, k2)={
%o A070180     if (  Mod(r,p)^((p-1)/gcd(k1,p-1))!=1, return(0) );
%o A070180     if (  Mod(r,p)^((p-1)/gcd(k2,p-1))==1, return(0) );
%o A070180     return(1);
%o A070180 }
%o A070180 forprime(p=2,10^4, if (ok(p,2,3,3^2),print1(p,", ")));
%o A070180 /* _Joerg Arndt_, Sep 21 2012 */
%Y A070180 Cf. A040028, A049596, A059262, A059667, A070179, A070181 - A070188.
%K A070180 nonn,easy
%O A070180 1,1
%A A070180 _Klaus Brockhaus_, Apr 29 2002