number theory - Modular Arithmetic and Fermat

Question: Find the smallest non-negative integer solution (if any exist) to the equation

$$x^{2017^2} + x^{2017} + 1 \equiv 0\mod\ 2017$$

Hint: You may use the fact that 2017 is a prime number. Fermat’s Theorem can help with this problem.

I have attempted to apply some addition rules to get

$$x^{2017^2} \equiv 0\mod 2017$$
$$x^{2017}\equiv 0\mod\ 2017$$

$$1 \equiv 0\mod\ 2017$$

and have gotten stuck. I have also tried to think about how $x^{2017^2} + x^{2017} + 1 = 2017n$ to satisfy the "$0\mod \ 2017$" portion but cannot get much further. I also am not quite sure how to successfully utilize Fermat's Theorem to solve this. I played around a bit but didn't get far.