Base-b Representations

Base-b Representations

For b > 1, the existence of base-b representations for positive integers is typically proved using either strong induction or the division algorithm, while uniqueness of the representation is typically obtained via a proof by contradiction. However, existence and uniqueness can be simultaneously...

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Veröffentlicht in:The American mathematical monthly 2019-10, Vol.126 (9), p.859-859
Hauptverfasser: Braun, Benjamin, de León, Santiago, Franz, Kyle, Sultan, Sami
Format: Artikel
Sprache:eng
Schlagworte:
Algorithms
MATHBITS
Mathematical models
Mathematical problems
MSC: Primary 05A17
Proof theory
Representations
Secondary 11P81
Uniqueness
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Beschreibung
Zusammenfassung:For b > 1, the existence of base-b representations for positive integers is typically proved using either strong induction or the division algorithm, while uniqueness of the representation is typically obtained via a proof by contradiction. However, existence and uniqueness can be simultaneously obtained through a short generating function argument.
ISSN:0002-9890
1930-0972
DOI:10.1080/00029890.2019.1647071