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A230309
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Sum_{0<=a<24*n, 0<=b<24*n} (a+b*i)^(24*n) (mod 24*n), where i is the imaginary unit.
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6
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8, 32, 0, 32, 80, 0, 56, 128, 0, 80, 176, 0, 104, 272, 0, 128, 272, 0, 152, 320, 0, 176, 368, 0, 200, 416, 0, 416, 464, 0, 248, 512, 0, 272, 560, 0, 296, 608, 0, 320, 656, 432, 344, 704, 0, 368, 752, 0, 392, 800, 0, 416, 848, 0, 560, 320, 0, 464, 944, 0, 488
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OFFSET
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1,1
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COMMENTS
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If m <> 0 (mod 24) then Sum_{(a+b*i)^m: 0<=a<m, 0<=b<m} == 0 (mod m).
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LINKS
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MATHEMATICA
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aa[n_] := aa[n] = Mod[Sum[PowerMod[a + b *I, n, n], {a, n}, {b, n}], n]; Table[aa[24*n], {n, 1, 10}]
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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