cp's OEIS Frontend

A070181 Primes p such that x^4 = 2 has a solution mod p, but x^(4^2) = 2 has no solution mod p.

%I A070181 #11 Sep 08 2022 08:45:05
%S A070181 113,281,353,577,593,617,1033,1049,1097,1153,1193,1201,1217,1249,1481,
%T A070181 1553,1601,1753,1777,1889,2129,2273,2281,2393,2473,2689,2833,2857,
%U A070181 3049,3089,3121,3137,3217,3313,3361,3529,3673,3761,3833,4001,4049,4153,4217
%N A070181 Primes p such that x^4 = 2 has a solution mod p, but x^(4^2) = 2 has no solution mod p.
%o A070181 (PARI) forprime(p=2,4250,x=0; while(x<p&&x^4%p!=2%p,x++); if(x<p,y=0; while(y<p&&y^(4^2)%p!=2%p,y++); if(y==p,print1(p,","))))
%o A070181 (Magma) [p: p in PrimesUpTo(5000) | not exists{x: x in ResidueClassRing(p) | x^16 eq 2} and exists{x: x in ResidueClassRing(p) | x^4 eq 2}]; // _Vincenzo Librandi_, Sep 21 2012
%o A070181 (PARI)
%o A070181 ok(p, r, k1, k2)={
%o A070181     if (  Mod(r,p)^((p-1)/gcd(k1,p-1))!=1, return(0) );
%o A070181     if (  Mod(r,p)^((p-1)/gcd(k2,p-1))==1, return(0) );
%o A070181     return(1);
%o A070181 }
%o A070181 forprime(p=2,10^5, if (ok(p,2,4,4^2),print1(p,", ")));
%o A070181 /* _Joerg Arndt_, Sep 21 2012 */
%Y A070181 Cf. A040098, A045315, A045316, A059667, A070179, A070180, A070182 - A070188.
%K A070181 nonn,easy
%O A070181 1,1
%A A070181 _Klaus Brockhaus_, Apr 29 2002