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MATH 440: Chapter 4 Write-Up Problems\vspace{1em}

Name:\vspace{1em}
\begin{enumerate}

\item Let $a$ be an element of a group $G$. Give, with proof, the generator of the subgroup $\langle a^m \rangle \cap \langle a^n\rangle$.

\item Prove or disprove: $\text{SL}_2(\mathbb{Z}_2)$ cyclic.

\item Solve for $x$. Explain your work and express your answer in the form of $a+bi$ for $a,b \in \mathbb{R}$.
$$-ix^2+2x+i+1 = 0.$$

\end{enumerate}

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