Let $f(x)$ be a function such that for all $x,$ $f(x) = f(x + 1) + f(x - 1).$  Given that $f(15) = 20$ and $f(20) = 15,$ compute $f(20152015).$
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<|im_start|>user
Let $f(x)$ be a function such that for all $x,$ $f(x) = f(x + 1) + f(x - 1).$  Given that $f(15) = 20$ and $f(20) = 15,$ compute $f(20152015).$
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
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Let $f(x)$ be a function such that for all $x,$ $f(x) = f(x + 1) + f(x - 1).$  Given that $f(15) = 20$ and $f(20) = 15,$ compute $f(20152015).$
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