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Primes p such that x^11 = 2 has a solution mod p, but x^(11^2) = 2 has no solution mod p.
3

%I #8 Sep 21 2012 02:44:51

%S 12101,13553,30493,32429,44771,66067,103577,128987,180533,182711,

%T 187793,201829,242243,257489,264749,299113,314359,330331,337349,

%U 341947,356467,371471,431729,442619,475289,484243,505781,513767,540871,558053,564103,573299,581527,582011,586367,593869,596047,630169

%N Primes p such that x^11 = 2 has a solution mod p, but x^(11^2) = 2 has no solution mod p.

%o (PARI) forprime(p=2,550000,x=0; while(x<p&&x^11%p!=2%p,x++); if(x<p,y=0; while(y<p&&y^(11^2)%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,2,11,11^2),print1(p,", ")));

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

%Y Cf. A049543, A059667, A070179 - A070186, A070188.

%K nonn

%O 1,1

%A _Klaus Brockhaus_, Apr 29 2002