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Primes p such that x^24 = 2 has no solution mod p, but x^12 = 2 has a solution mod p.
2

%I #10 Sep 08 2022 08:45:02

%S 113,281,353,593,617,1049,1097,1193,1481,1601,1753,1889,2129,2273,

%T 2281,2393,2689,3089,3137,3761,3833,4001,4153,4217,4289,4457,4657,

%U 4817,4937,5113,5393,5569,6521,6569,6761,7481,7577,7793,7817,7841,8273,8369,8537

%N Primes p such that x^24 = 2 has no solution mod p, but x^12 = 2 has a solution mod p.

%H Vincenzo Librandi, <a href="/A059331/b059331.txt">Table of n, a(n) for n = 1..370</a>

%t Select[Prime[Range[PrimePi[1000]]], !MemberQ[PowerMod[Range[#], 24, #], Mod[2, #]] && MemberQ[PowerMod[Range[#], 12, #], Mod[2, #]]&] (* _Vincenzo Librandi_, Sep 21 2013 *)

%o (Magma) [p: p in PrimesUpTo(9000) | not exists{x: x in ResidueClassRing(p) | x^24 eq 2} and exists{x: x in ResidueClassRing(p) | x^12 eq 2}]; // _Vincenzo Librandi_, Sep 21 2012

%Y A000040, A049556, A049544, A059264.

%K nonn,easy

%O 1,1

%A _Klaus Brockhaus_, Jan 26 2001