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anemone

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Denote by $f^n(x)$ the result of applying the function $f$ $n$ times to $x$ (e.g. $f^1(x)=f(x),\,f^2(x)=f(f(x)),\,f^3(x)=f(f(f(x)))$ Find all functions from real numbers to real numbers which satisfy $f^d(x)=2015-x$ for all divisors $d$ of 2015, which are greater than 1, and for all real $x$.

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