###### tags: `MATA02-2022`
# Ungraded problems 10

You are to work on these questions only for the benefit of learning the material. These problems are meant for practice, not an assignment to be handed in.

**Only two of the following four problems can be solved with the method described in the lectures using Fermat's Little Theorem. Say which they are, and do them.**)

## 1.
Find the fifth root of 3 in arithmetic modulo 23.
\begin{equation}
\sqrt[5]{3} \hspace{1em} \text{ (mod 23)}
\end{equation}

## 2.
Find the fifth root of 7 in arithmetic modulo 31.
\begin{equation}
\sqrt[5]{7} \hspace{1em} \text{ (mod 31)}
\end{equation}

## 3.
Find the cube root of 4 in arithmetic modulo 57.
\begin{equation}
\sqrt[3]{4} \hspace{1em} \text{ (mod 57)}
\end{equation}

## 4.
Find the cube root of 4 in arithmetic modulo 59.
\begin{equation}
\sqrt[3]{4} \hspace{1em} \text{ (mod 59)}
\end{equation}

# Selected (partial) solutions
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<summary>Solutions (click to expand)</summary>


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