Abstract
For a given rational number r, a classical theorem of Niven asserts that if is rational, then
In this note, we extend Niven's theorem to quadratic irrationalities and present an elementary proof of that.
Acknowledgments
The author would like to thank the anonymous referees for their insightful comments, which greatly help to improve the exposition of this paper.
Disclosure statement
No potential conflict of interest was reported by the author.