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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! –  GYC Jan 28 '13 at 6:01
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up vote 6 down vote accepted

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 $p-1$.

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Thank you very much for the link. –  Mohan Jan 28 '13 at 6:10
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