A dynamical system proof of Niven's theorem and its extensions

Chatchawan Panraksa; Detchat Samart; Songpon Sriwongsa

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arXiv · 2304.07823

A dynamical system proof of Niven's theorem and its extensions

Chatchawan Panraksa·Detchat Samart·Songpon Sriwongsa

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Abstract

Niven's theorem asserts that $\{\cos(r\pi) \mid r\in \mathbb{Q}\}\cap \mathbb{Q}=\{0,\pm 1,\pm 1/2\}.$ In this paper, we use elementary techniques and results from arithmetic dynamics to obtain an algorithm for classifying all values in the set $\{\cos(r\pi) \mid r\in \mathbb{Q}\}\cap K$, where $K$ is an arbitrary number field.

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Chatchawan Panraksa, Detchat Samart, Songpon Sriwongsa. 2023-04-16. A dynamical system proof of Niven's theorem and its extensions. https://arxiv.org/abs/2304.07823

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