# A recurrence relation

Let $$a_0,a_1,\cdots$$ be a sequence defined by $$a_0=7$$, $$a_1=8$$, and, for all $$n\ge 2$$, $a_n=5a_{n-1}-6a_{n-2}$ Find the remainder when $$a_{2014}$$ is divided by 1000.

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