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