# Sequence

Algebra Level 5

The sequences $$\{a_n\}_{n=1}^\infty$$ and $$\{b_n\}_{n=1}^\infty$$ are defined through $$a_1=\alpha$$, $$b_1=\beta$$, $$a_{n+1}=\alpha a_n-\beta b_n$$, and $$b_{n+1}=\beta a_n+\alpha b_n$$ for all $$n\ge2$$. How many pairs of real numbers $$(\alpha,\beta)$$ are there such that $$a_{2014}=b_1$$ and $$b_{2014}=a_1$$?

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