The argument of Böhm and Sontacchi is a very general one that makes use only of the fact that the necessary condition (2.24) for a cycle has a unique solution when the values are fixed. In fact, considerably more can be proved about the nonexistence of nontrivial cyclic trajectories using special features of the necessary condition (2.24). For example, several authors have independently found a much more efficient computational procedure for proving the nonexistence of nontrivial cyclic trajectories of period ; it essentially makes use of the inequality

which must hold for satisfying (2.24). This approach also allows one to check the truth of the Coefficient Stopping Time Conjecture for all n with . The basic result is as follows.
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