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If sum(k=0)^n ( a + b w^k) (b + c w^k) (...

If `sum_(k=0)^n ( a + b w^k) (b + c w^k) ( c+ aw^k)` is purely a real number, when a,b,c are distinct real numbers and w is a complex root of unity, then which of the following cannot be the value of n :

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