# It's still 2014!

Algebra Level 5

Let $$\alpha$$ and $$\beta$$ be the roots of $$x^2-6x-2=0$$, with $$\alpha >\beta$$. If $$a_n=\alpha^n-\beta^n$$ for $$n\geq 1$$, then $k=\dfrac{a_{10}-2a_8}{2a_9}$ Then find the remainder when $$k^{942}$$ is divided by $$2014$$.

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