A070182 - OEIS

%I #11 Sep 08 2022 08:45:05

%S 151,251,3251,3301,4751,8501,11251,11701,13751,14251,14951,15551,

%T 16451,17401,18401,21401,21601,24251,28351,28901,32251,32401,32801,

%U 34301,36151,36451,37201,40351,42451,42701,44201,45751,46051,46451,46901

%N Primes p such that x^5 = 2 has a solution mod p, but x^(5^2) = 2 has no solution mod p.

%o (PARI) forprime(p=2,47000,x=0; while(x<p&&x^5%p!=2%p,x++); if(x<p,y=0; while(y<p&&y^(5^2)%p!=2%p,y++); if(y==p,print1(p,","))))

%o (Magma) [p: p in PrimesUpTo(50000) | not exists{x: x in ResidueClassRing(p) | x^25 eq 2} and exists{x: x in ResidueClassRing(p) | x^5 eq 2}]; // _Vincenzo Librandi_, Sep 21 2012

%o (PARI)

%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=2,10^5, if (ok(p,2,5,5^2),print1(p,", ")));

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

%Y Cf. A040159, A049557, A059313, A059667, A070179 - A070181, A070183 - A070188.

%K nonn,easy

%O 1,1

%A _Klaus Brockhaus_, Apr 29 2002