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
by
Aneesh Kundu