# Brilliant Number theoretical Functional Equations

Define a function $$f : \mathbb{Z} \rightarrow \{1,2,...,2017 \}$$ to be brilliant if for any integer $$n$$ where $$1 \leq n \leq 2016$$ there exists a certain integer $$p(n)$$ so that we have:

$$f(m + p(n)) \equiv f(m +n) - f(m) \pmod{2018}$$

Find the number of brilliant functions.

Details and assumptions - 2017 is prime. - This is not an original problem. This has been modified from a competition problem whose source I have forgotten.

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