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1 solution
3 n = 0 ∑ 3 0 0 0 ( 3 n 9 0 0 0 ) = 3 3 ( 1 + 1 ) 9 0 0 0 + ( 1 + ω ) 9 0 0 0 + ( 1 + ω 2 ) 9 0 0 0 = 3 3 2 9 0 0 0 + ( − ω 2 ) 9 0 0 0 + ( − ω ) 9 0 0 0 = 3 3 ( 2 9 0 0 0 + 1 + 1 ) = 2 9 0 0 0 + 2 2 9 0 0 0 + 2 > 2 9 0 0 0
ω is a third root of unity.