# Sum it up to 1729

Algebra Level 4

If $$V_{n}=a^{n}+b^{n},$$ where $$a$$ and $$b$$ are the roots of $$x^{2}+x+1,$$ what is the value of $\sum_{n=0}^{1729} (-1)^{n} \cdot \ V_{n} ?$

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