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Numbers k such that k^4 == 1 (mod 5^5).
0

%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