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**
Powers of Two Modulo Powers of Three
**

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Michael Coons and Heath Winning

School of Mathematical and Physical Sciences

The University of Newcastle

Callaghan, NSW

Australia

**Abstract:**

Since 2 is a primitive root of 3^{m}
for each positive integer *m*,
the set of points
{ (*n*, 2^{n} mod 3^{m}) : *n* ≥ 0},
viewed as a subset of
**Z**_{≥ 0} × **Z**_{≥ 0}
is
bi-periodic, with minimal periods ϕ(3^{m})
(horizontally) and
3^{m} (vertically).
We show that if one considers the classes of *n*
modulo 6, one obtains a finer structural classification. This result
is presented within the context of the question of strong normality of
Stoneham numbers.

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(Concerned with sequences
A000079
A000244.)

Received
May 11 2015; revised version received May 18 2015.
Published in *Journal of Integer Sequences*, May 29 2015.

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