Circular Tracks

Several cars, conveniently numbered 0 to N, are driving in different lanes on a circular track. For i between 0 and N-1, if the driver in car i looks straight ahead, he always sees car i+1. If the driver in car N looks directly at the center of the track, he always sees car 0. What are the possible values of (s,k,N) for which this holds true if the speed of car i is:
  1. s+ki?
  2. s*(k^i)?
For example, this will work in case 2 if k=2 and N=6. Each car will be progressively 60 degrees farther around the track.

Source: Original.

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