Question 154
Denote by $f^n(x)$ the result of applying the function $f$ $n$ times to $x$ (e.g. $f^1(x) = f(x)$, $f^2(x) = f(f(x))$, $f^3(x) = f(f(f(x)))$ etc). 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 $x$.