There's Cubic Residues As Well?

\[x^3\equiv 1 \pmod{2016}\]

How many positive integer solutions \(x<2016\) does the above congruency have?

Bonus Problem: Looking ahead, what about \(x^3\equiv 1 \pmod{2017}\) or even \(x^3\equiv 1 \pmod{2017^{2017}}\)?

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