Exercise 1.

In this exercise, detailed and precise explanations are required. As expected, we consider the field ${\mbox{${\mathbb{K}}$}} = {\mbox{${\mathbb{Z}}$}}/17{\mbox{${\mathbb{Z}}$}}$ .

1. Show that 3 is in ${\mathbb{K}}$ a primitive 16-th root of unity.
2. Find all primitive 4-th roots of unity in ${\mathbb{K}}$ .

Answer 1  

Answer 2