A DYNAMICAL SYSTEM PROOF OF NIVEN’S THEOREM AND ITS EXTENSIONS

Journal article

Authors/Editors

SONGPON SRIWONGSA

Strategic Research Themes

Digital Transformation (Strategic Research Themes)

Publication Details

Author list: CHATCHAWAN PANRAKSA , DETCHAT SAMART and SONGPON SRIWONGSA

Publisher: Cambridge University Press

Publication year: 2024

Volume number: 109

Issue number: 1

Start page: 138

End page: 151

Number of pages: 14

ISSN: 0004-9727

eISSN: 1755-1633

URL: https://www.cambridge.org/core/journals/bulletin-of-the-australian-mathematical-society/article/dynamical-system-proof-of-nivens-theorem-and-its-extensions/25902DFDB28FF3618279FA9043930016

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Abstract

Niven’s theorem asserts that {cos(rπ) | r ∈ Q} ∩ Q = {0, ±1, ±1/2}. In this paper, we use elementary
techniques and results from arithmetic dynamics to obtain an algorithm for classifying all values in the set
{cos(rπ) | r ∈ Q} ∩ K, where K is an arbitrary number field.

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