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Let α\alphaα and β\betaβ be the roots of x2−6x−2=0x^2-6x-2=0x2−6x−2=0, with α>β\alpha >\betaα>β. If an=αn−βna_n=\alpha^n-\beta^nan=αn−βn for n≥1n\geq 1n≥1, then k=a10−2a82a9k=\dfrac{a_{10}-2a_8}{2a_9}k=2a9a10−2a8 Then find the remainder when k942k^{942}k942 is divided by 201420142014.
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