%I #29 Feb 24 2024 01:07:21

%S 2,6,7,11,15,19,20,24,28,32,33,37,41,45,46,50,54,58,59,63,67,71,72,76,

%T 80,84,85,89,93,97,98,102,106,110,111,115,119,123,124,128,132,136,137,

%U 141,145,149,150,154,158,162,163,167,171,175,176,180,184,188,189,193

%N Solutions x to x^n == 7 mod 13.

%D E. Grosswald, Topics From The Theory of Numbers, 1966, pp. 62-63.

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,1,-1).

%F G.f.: x*(2 + 4*x + x^2 + 4*x^3 + 2*x^4)/(1 - x - x^4 + x^5). - _Philippe Deléham_, Dec 01 2016

%e 2^11 - 7 = 2041 = 11*157. Thus 2 is in the sequence.

%t LinearRecurrence[{1, 0, 0, 1, -1},{2, 6, 7, 11, 15},60] (* _Ray Chandler_, Aug 25 2015 *)

%o (PARI) conxkmap(a,p,n) = { for(x=1,n, for(j=1,n, y=x^j-a; if(y%p==0,print1(x","); break) ) ) }

%o (Magma) I:=[2,6,7,11,15]; [n le 5 select I[n] else Self(n-1)+Self(n-4)-Self(n-5): n in [1..70]]; // _Vincenzo Librandi_, Dec 02 2016

%K nonn,easy

%O 1,1

%A _Cino Hilliard_, Nov 03 2003