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