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Writing Numbers in Base \(3\), the Hard Way

by Gary E. Michalek

This article originally appeared in:
Mathematics Magazine
February, 2001

Subject classification(s): Algebra and Number Theory | Number Theory | Integers
Applicable Course(s): 4.3 Number Theory

Every integer can be expressed in base \(2\) using the set \(\{-1, 0, 1\}\) as coefficients. Does one need to use this set, or might another set of numbers do as well? The author investigates this type of question in base \(3\), to provide richer examples.

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Capsule Course Topic(s):
Number Theory | Numbers With Special Forms or Properties, Base Representation and Decimal Expansion
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