# Compositional Square

Define a function $$\displaystyle f(n) = n + \left \lfloor \sqrt{n} \right \rfloor$$.

Find the smallest value of $$k$$ such that the composite function,
$$f^{k} (2017) = \underbrace{f\circ f \circ f \circ \cdots \circ f}_{k \text{ times}} (2017)$$ can be expressed as $$m^2$$ for some positive integer $$m$$.

Submit your answer as $$m-k$$.

 Notation: $$\lfloor \cdot \rfloor$$ denotes the floor function.

×