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**[SOLVED] Cyclic Sequence of Angles**

Fix an angle [itex]\theta[/itex]. Let n be a positive integer and define [itex]\theta_n = n\theta \bmod 2\pi[/itex].

The sequence [itex]\theta_1, \theta_2, \ldots[/itex] is cyclic if if it starts repeating itself at some point, i.e. the sequence has the form [itex]\theta_1, \ldots, \theta_k, \theta_1 \ldots[/itex].

What I would like to find out is: For which angles [itex]\theta[/itex] is the sequence [itex]\{\theta_n\}[/itex] cyclic? If for some integer m > 1, [itex]\theta_1 = \theta_m \equiv \theta = m\theta[/itex], then [itex]m\theta = \theta + 2\pi x[/itex] for some non-negative integer x. Solving for [itex]\theta[/itex], I get [itex]\theta = 2\pi x / (m - 1)[/itex]. So it seems that any rational multiple of [itex]\pi[/itex] will create a cyclic sequence. Is this correct?