Question 121
Find all integers $c \in \{0, 1, \dots, 2016\}$ for which the number of functions $f: Z \rightarrow \{0, 1, \dots, 2016\}$ satisfying the following two conditions is minimal:
(1) the function $f$ has period $2017$;
(2) $f(f(x) + f(y) + 1) - f(f(x) + f(y)) \equiv c \pmod{2017}$.
Note: Here $Z$ denotes the set of all integers.
(1) the function $f$ has period $2017$;
(2) $f(f(x) + f(y) + 1) - f(f(x) + f(y)) \equiv c \pmod{2017}$.
Note: Here $Z$ denotes the set of all integers.