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A230309 Sum_{0<=a<24*n, 0<=b<24*n} (a+b*i)^(24*n) (mod 24*n), where i is the imaginary unit.

%I A230309 #25 Dec 25 2023 17:49:51
%S A230309 8,32,0,32,80,0,56,128,0,80,176,0,104,272,0,128,272,0,152,320,0,176,
%T A230309 368,0,200,416,0,416,464,0,248,512,0,272,560,0,296,608,0,320,656,432,
%U A230309 344,704,0,368,752,0,392,800,0,416,848,0,560,320,0,464,944,0,488
%N A230309 Sum_{0<=a<24*n, 0<=b<24*n} (a+b*i)^(24*n) (mod 24*n), where i is the imaginary unit.
%C A230309 If m <> 0 (mod 24) then Sum_{(a+b*i)^m: 0<=a<m, 0<=b<m} == 0 (mod m).
%H A230309 Amiram Eldar, <a href="/A230309/b230309.txt">Table of n, a(n) for n = 1..1000</a>
%t A230309 aa[n_] := aa[n] = Mod[Sum[PowerMod[a + b *I, n, n], {a, n}, {b, n}], n]; Table[aa[24*n],{n,1,10}]
%o A230309 (PARI) a(n)=my(N=24*n,a);lift(sum(A=0,N-1,a=Mod(A,N);sum(b=0,N-1,(a+b*I)^N))) \\ _Charles R Greathouse IV_, Nov 05 2013
%Y A230309 Cf. A230308, A230310.
%K A230309 nonn
%O A230309 1,1
%A A230309 _José María Grau Ribas_, Oct 16 2013