cp's OEIS Frontend

A070186 Primes p such that x^10 = 2 has a solution mod p, but x^(10^2) = 2 has no solution mod p.

%I A070186 #11 Sep 08 2022 08:45:05
%S A070186 17,97,137,151,193,241,313,409,433,449,457,569,641,673,769,809,857,
%T A070186 929,953,977,1009,1129,1297,1409,1489,1657,1697,1873,1993,2017,2137,
%U A070186 2153,2297,2377,2417,2609,2617,2633,2713,2729,2753,2777,2897,2953,3169,3209
%N A070186 Primes p such that x^10 = 2 has a solution mod p, but x^(10^2) = 2 has no solution mod p.
%o A070186 (PARI) forprime(p=2,3300,x=0; while(x<p&&x^10%p!=2%p,x++); if(x<p,y=0; while(y<p&&y^(10^2)%p!=2%p,y++); if(y==p,print1(p,","))))
%o A070186 (Magma) [p: p in PrimesUpTo(3500) | not exists{x: x in ResidueClassRing(p) | x^100 eq 2} and exists{x: x in ResidueClassRing(p) | x^10 eq 2}]; // _Vincenzo Librandi_, Sep 21 2012
%o A070186 (PARI)
%o A070186 ok(p, r, k1, k2)={
%o A070186     if (  Mod(r,p)^((p-1)/gcd(k1,p-1))!=1, return(0) );
%o A070186     if (  Mod(r,p)^((p-1)/gcd(k2,p-1))==1, return(0) );
%o A070186     return(1);
%o A070186 }
%o A070186 forprime(p=2,10^5, if (ok(p,2,10,10^2),print1(p,", "))); \\ A070186
%o A070186 /* _Joerg Arndt_, Sep 21 2012 */
%Y A070186 Cf. A049542, A059667, A070179 - A070185, A070187, A070188.
%K A070186 nonn,easy
%O A070186 1,1
%A A070186 _Klaus Brockhaus_, Apr 29 2002