Author: mathforces
Problem has been solved: 9 times

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Let $F_ {2017}$ be the set of all remainders when dividing by $2017$. The function $f: Z-> F_ {2017}$ is called administrative if there exists $a \in F_ {2017}$, $a \neq 0$ such that $f (x) f (y) = f (x + y) + a ^ yf (x-y) \ \ (mod \ \ 2017)$ for all $x, y \ in Z$. Find the number of administrative, periodic functions with the smallest period of 2016?