# Periodic fixed point

Algebra Level 5

Consider the sequence: $$x_{n+1} = 4x_n(1 − x_n)$$

Call a point $$x_0\in[0, 1]$$ is $$r−$$periodic if $$x_r=x_0$$. For example, $$x_0 = 0$$ is always a $$r−$$periodic fixed point for any $$r$$.

Let $$N$$ be the number of positive $$2015−$$periodic fixed points.

Find the last 3 digits of $$N$$.

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