###### tags: `MATA02-2022`
# MATA02-2022: Graded Assignment 5
**DUE: Friday, April 1, 11:59pm**

## 1.
One of the techniques you learned in class for finding unique roots relied on Fermat's Little Theorem.

Find if each of the following four problems can be solved with the method using Fermat's Little Theorem. If it is, solve it; if not, say why not.

1. $\sqrt[7]{3}$ mod 23
2. $\sqrt[7]{7}$ mod 31
3. $\sqrt[3]{5}$ mod 97
4. $\sqrt[11]{7}$ mod 61

## 2.
Find at least one solution to each of the following root problems. Note that you may need to use the more powerful method we learned using Euler's Theorem.
1. $\sqrt[17]{8}$ mod 57
2. $\sqrt[25]{7}$ mod 65
3. $\sqrt[9]{11}$ mod 85