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For the specified parameter relation,Thus there are $|n|$ axial oscillations per transverse revolution, and the nondegenerate three-dimensional trajectory closes after $2\pi /{\Omega }_c$. Since $\lambda >0$, the integer $n=0$ is excluded; changing its sign changes nothing. More generally commensurate cyclotron and axial oscillations close for any rational frequency ratio, whereas irrational ratios give quasiperiodic motion when both components are present. An integer ratio is sufficient, not the only closure condition. The same frequency argument also applies to transverse cyclotron circles centred away from the chosen cylindrical origin.