The Coefficient Stopping Time Conjecture has the aesthetic appeal that if it is true, then the set of positive integers with stopping time k is exactly a collection of congruence classes , as described by part (i) of Theorem C. Furthermore, the truth of the Coefficient Stopping Time Conjecture implies that there are no nontrivial cycles. To see this, suppose that there were a nontrivial cycle of period k and let be its smallest element, and note that . Then for and


Now since isn't a power of 2, so that (2.20) implies that . Hence , so that .
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