Question 7
Let $\mathbb{N}$ denote the natural numbers. Compute the number of functions $f: \mathbb{N} \rightarrow \{0,1, \ldots, 16\}$ such that
$$
f(x+17)=f(x) \quad \text{and} \quad f\left(x^{2}\right) \equiv f(x)^{2}+15 \pmod{17}
$$
for all integers $x \geq 1$.
$$
f(x+17)=f(x) \quad \text{and} \quad f\left(x^{2}\right) \equiv f(x)^{2}+15 \pmod{17}
$$
for all integers $x \geq 1$.