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Reading Questions 4.4 Reading Questions

1.

What is the order of the element \(3\) in \(U(20)\text{?}\)

2.

What is the order of the element \(5\) in \(U(23)\text{?}\)

3.

Find three generators of \(\mathbb Z_8\text{.}\)

4.

Find three generators of the \(5^\text{th}\) roots of unity.

5.

Show how to compute \(15^{40}\pmod{23}\) efficiently by hand. Check your answer with Sage.