Is there a way of finding a generator of a multiplicative group $G = \mathbb{Z}_{41723027}^\times$ given some elements of the group :
S = $\{ 4, y=1063, 1064, y^{-1}=12049830, 41723026 \}$
In the exersice it says as additional information that there is exactly one generator in this set.
Can you explain me why there is only one generator and give some outline of the method I should use to find this generator?