# Functionally, a Number theory problem

Number Theory Level 4

An increasing function $$f: \mathbb{N} ^{ \geq 0 } \rightarrow \mathbb{N} ^{ \geq 0 }$$ satisfies $$f(2) = 7$$ and

$f(mn) = f(m) + f(n) + f(m)f(n) \text{ for all } m, n \in \mathbb{N} ^{ \geq 0 }.$

Find the remainder when $$f(2017)$$ is divided by $$2017$$.

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