It's still 2014!

Algebra Level 5

Let α\alpha and β\beta be the roots of x26x2=0x^2-6x-2=0, with α>β\alpha >\beta. If an=αnβna_n=\alpha^n-\beta^n for n1n\geq 1, then k=a102a82a9k=\dfrac{a_{10}-2a_8}{2a_9} Then find the remainder when k942k^{942} is divided by 20142014.


Note

  • Something amazing happens when you add 1000 to the answer
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