Find all possible integer values of $n$ such that the following system of equations has a solution for $z$: \begin{align*} z^n &= 1, \\ \left(z + \frac{1}{z}\right)^n &= 1. \end{align*}

The perimeter of an equilateral triangle is 4 cm more than the perimeter of a square and the length of a side of the triangle is 8 cm more than the length of a side of the aware. find the length of a side of the equilateral triangle