Hw5 Problem 2

### Problem 2

Write at least five elements of each of the following cyclic groups.

(1) $14 \mathbb Z$ under addition.
(2) $\langle$ $( \frac{2}{3} )$ $\rangle$ $= \{ ( \frac{2}{3} ) ^n \mid n \in \mathbb Z \}$.

Solution

(1) $14,28,42,56,70.$

(2) $\frac{2}{3}, \frac{4}{9}, \frac{8}{27}, \frac{16}{81}, \frac{32}{243}.$