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 $2014$ .

Note

Something amazing happens when you add 1000 to the answer