# Generators for $\mathbb F_p^*$

Let $p$ be prime, then it is a well-known fact that $\mathbb F_p^*= \mathbb F_p -\{0\}$ is a cyclic group under multiplication. Are there any methods to determine the generators of this cyclic or any results which help in actually finding the generators?

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I like this question a lot! – user123454321 Jan 28 '13 at 6:01

See chapter 11 of Shoup's A Computational Introduction to Number Theory and Algebra. In general this is a difficult problem, but there's a good probabilistic algorithm if you can factor $p-1$.