cp's OEIS Frontend

A070185 Primes p such that x^9 = 2 has a solution mod p, but x^(9^2) = 2 has no solution mod p.

%I A070185 #7 Sep 21 2012 02:46:33
%S A070185 3943,5347,11287,12853,14149,17659,20143,21061,21277,23059,23599,
%T A070185 25759,26407,26731,29863,32833,33751,35803,37747,38287,39367,39799,
%U A070185 46441,47737,47791,54919,57781,59887,61291,62047,63127,65557,68311,71443,73063,75169,78301,79273,82351,84457,84673,86077,88129,90289
%N A070185 Primes p such that x^9 = 2 has a solution mod p, but x^(9^2) = 2 has no solution mod p.
%o A070185 (PARI) forprime(p=2,72000,x=0; while(x<p&&x^9%p!=2%p,x++); if(x<p,y=0; while(y<p&&y^(9^2)%p!=2%p,y++); if(y==p,print1(p,","))))
%o A070185 (PARI)
%o A070185 N=10^6;  default(primelimit,N);
%o A070185 ok(p, r, k1, k2)={
%o A070185     if (  Mod(r,p)^((p-1)/gcd(k1,p-1))!=1, return(0) );
%o A070185     if (  Mod(r,p)^((p-1)/gcd(k2,p-1))==1, return(0) );
%o A070185     return(1);
%o A070185 }
%o A070185 forprime(p=2,N, if (ok(p,2,9,9^2),print1(p,", ")));
%o A070185 /* _Joerg Arndt_, Sep 21 2012 */
%Y A070185 Cf. A049596, A059667, A070179 - A070184, A070186 - A070188.
%Y A070185 Cf. A059354.
%K A070185 nonn
%O A070185 1,1
%A A070185 _Klaus Brockhaus_, Apr 29 2002