Sum it up to 1729

Algebra Level 4

If Vn=an+bn,V_{n}=a^{n}+b^{n}, where aa and bb are the roots of x2+x+1,x^{2}+x+1, what is the value of

n=01729(1)n Vn? \sum_{n=0}^{1729} (-1)^{n} \cdot \ V_{n} ?

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