# I swear I'm sleeping

Number Theory Level 3

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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