%I #17 Aug 20 2023 16:57:17
%S 1,1068,2057,3124,3126,4193,5182,6249,6251,7318,8307,9374,9376,10443,
%T 11432,12499,12501,13568,14557,15624,15626,16693,17682,18749,18751,
%U 19818,20807,21874,21876,22943,23932,24999,25001,26068,27057,28124
%N Numbers k such that k^4 == 1 (mod 5^5).
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,1,-1).
%F From _Chai Wah Wu_, Jun 21 2020: (Start)
%F a(n) = a(n-1) + a(n-4) - a(n-5) for n > 5.
%F G.f.: x*(x^4 + 1067*x^3 + 989*x^2 + 1067*x + 1)/(x^5 - x^4 - x + 1). (End)
%t x=5; Select[ Range[ 50000 ], PowerMod[ #, x-1, x^5 ]==1& ]
%o (PARI) for(n=1,30000,if(n^4%5^5==1,print1(n,", "))) \\ _Hugo Pfoertner_, Jun 21 2020
%K nonn,easy
%O 1,2
%A _Robert G. Wilson v_, Jun 08 2000