Nguyen Xuan Tho
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 28, 2022, Number 1, Pages 75–80
Download PDF (169 Kb)
Authors and affiliations
We show that if is a positive integer such that for each positive integer , can be expressed , where , then is a square number. A similar theorem also holds if and are replaced by and , respectively.
- Elementary number theory
- Square numbers
- Quadratic reciprocity
2020 Mathematics Subject Classification
- Ireland, K., & Rosen, M. (1998). A Classical Introduction to Number Theory (2nd ed.). Springer.
- Wang, S. (1950). On Grunwald’s theorem, Annals of Mathematics, Second Series, 51(2), 471–484.
- Received: 2 February 2021
- Revised: 16 November 2021
- Accepted: 11 February 2022
- Online First: 14 February 2022
Cite this paper
Tho, N. X. (2022). Two theorems on square numbers. Notes on Number Theory and Discrete Mathematics, 28(1), 75-80, DOI: 10.7546/nntdm.2022.28.1.75-80.