Excel in math, science, and engineering

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Define a sequence \(\lbrace a_{n} \rbrace\) by the linear reccurence \(a_{n} = 5a_{n-1}-6a_{n-2}\), with \(a_{1} = 8\) and \(a_{2} = 21\).

Find \(a_{6001} \pmod{7}\).

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