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Theorem C shows that generally they are equal:
For any fixed **k** at most a finite number of those **n** having coefficient
stopping time have .
Terras [67]
and later Garner [34] conjecture that this never occurs.

###
COEFFICIENT STOPPING TIME CONJECTURE.

* For all , the stopping time equals the
coefficient stopping time .*
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
.
The following result shows that the Coefficient Stopping Time Conjecture is
``nearly true.''
I will use it later to bound the number of elements not having a finite stopping time.

### Theorem E

* There is an effectively computable constant such that if is
admissible of length , then all elements of
have stopping time ***k** except possibly the smallest element
of **S**.

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