If I have(adsbygoogle = window.adsbygoogle || []).push({}); nrunners on a circular tracks at different speeds [itex]s_i[/itex], will they always meet up arbitrarily close together in a group?

So does there always exist a timetsuch that

[tex]

\forall i,\varepsilon>0 ,\exists t: [t\cdot s_i]<\varepsilon

[/tex]

where the bracket denote the fractional (non-integer) part.

And if that time always exists, what is the combination of runner speeds such that it takes them longest time to meet up again?

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# Alignments of runners

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