Order of a power of an element

Suppose $G$ is a cyclic group of finite order $n$ , and $t \in G$ is a generator.

Give a positive integer $d$ such that $t^{- 1} = t^{d}$ .
Let $c$ be an integer and let $m = gcd (n, c)$ . Prove that the order of $t^{c}$ is $\frac{n}{m}$ .

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Suppose $G$ is a cyclic group of order $n$, and $t\in G$ is a generator.
\begin{enumerate}[label=\alph*)]
	\item Give a positive integer $d$ such that $t^{-1}=t^d$.
	\item Let $c$ be an integer and let $m=\gcd(n,c)$. Prove that the order of $t^c$ is $\frac{n}{m}$.
\end{enumerate}