This is a question that was asked in my group theory examination today:
Let $G$ be a finite cyclic group generated by an element $x$ of $G$. If $y(\ne x)\in G$ is also a generator of $G$, find the relation between the elements $x$ and $y$.
I do not think that given an arbitrary finite cyclic group one can give a nice relation between any two of its generators. For example if $\mathbb{Z}/50\mathbb{Z}$ what is the relation between 7 and 49 or 23 and 31 or say 3 and 43? I have not been able to understand clearly what kind of a relation the question asks for. I know that $x=y^m$ for some $m$, and $m$ is then coprime to the order of the group but I do not know how could this give a relation involving only $x$ and $y$. So what is the question asking for and what in general is a relation between $x$ and $y$?