# Good luck counting them all

**Number Theory**Level 5

How many different regular pair-wise non-similar \(2^{74207281} -1\) sided polygons with fixed side length exist if self-intersecting is allowed?

Express your answer in form \(2^{n} - 1\), submit \(\varphi(n+1)\). (Euler's Totient Function of \(n+1\))

**Note:** \(2^{74207281} -1\) is the largest known Mersenne Prime.

**Bonus:** Generalize this for any number of sides.