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

Chatchawan Panraksa, Detchat Samart, Songpon Sriwongsa

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 dynamic…