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A049561 Primes p such that x^29 = 2 has a solution mod p.

%I A049561 #18 Jul 20 2025 08:18:40
%S A049561 2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,61,67,71,73,79,83,89,97,
%T A049561 101,103,107,109,113,127,131,137,139,149,151,157,163,167,173,179,181,
%U A049561 191,193,197,199,211,223,227,229,239,241,251,257,263,269,271,277,281
%N A049561 Primes p such that x^29 = 2 has a solution mod p.
%C A049561 Complement of A059256 relative to A000040. - _Vincenzo Librandi_, Sep 14 2012
%H A049561 R. J. Mathar, <a href="/A049561/b049561.txt">Table of n, a(n) for n = 1..1000</a>
%H A049561 <a href="/index/Pri#smp">Index entries for related sequences</a>
%e A049561 0^29 == 2 (mod 2). 2^29 == 2 (mod 3). 2^29 == 2 (mod 5). 4^29 == 2 (mod 7). 6^29 == 2 (mod 11). 6^29 == 2 (mod 13). 15^29 == 2 (mod 17). 13^29 == 2 (mod 19). 3^29 == 2 (mod 23). 2^29 == 2 (mod 29). 16^29 == 2 (mod 31). 32^29 == 2 (mod 37). 20^29 == 2 (mod 41). 2^29 == 2 (mod 43). - _R. J. Mathar_, Jul 20 2025
%t A049561 ok[p_]:= Reduce[Mod[x^29 - 2, p] == 0, x, Integers] =!= False; Select[Prime[Range[100]], ok] (* _Vincenzo Librandi_, Sep 14 2012 *)
%o A049561 (Magma) [p: p in PrimesUpTo(300) | exists(t){x : x in ResidueClassRing(p) | x^29 eq 2}]; // _Vincenzo Librandi_, Sep 14 2012
%Y A049561 Cf. A000040, A059256.
%K A049561 nonn,easy
%O A049561 1,1
%A A049561 _N. J. A. Sloane_