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Primes p such that x^9 = 2 has a solution mod p, but x^(9^2) = 2 has no solution mod p.
4

%I #7 Sep 21 2012 02:46:33

%S 3943,5347,11287,12853,14149,17659,20143,21061,21277,23059,23599,

%T 25759,26407,26731,29863,32833,33751,35803,37747,38287,39367,39799,

%U 46441,47737,47791,54919,57781,59887,61291,62047,63127,65557,68311,71443,73063,75169,78301,79273,82351,84457,84673,86077,88129,90289

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

%o (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 (PARI)

%o N=10^6; default(primelimit,N);

%o ok(p, r, k1, k2)={

%o if ( Mod(r,p)^((p-1)/gcd(k1,p-1))!=1, return(0) );

%o if ( Mod(r,p)^((p-1)/gcd(k2,p-1))==1, return(0) );

%o return(1);

%o }

%o forprime(p=2,N, if (ok(p,2,9,9^2),print1(p,", ")));

%o /* _Joerg Arndt_, Sep 21 2012 */

%Y Cf. A049596, A059667, A070179 - A070184, A070186 - A070188.

%Y Cf. A059354.

%K nonn

%O 1,1

%A _Klaus Brockhaus_, Apr 29 2002