Notes on the sequence ⌊ mα ⌋ for irrational α
Abstract
The sequence ⌊mα⌋, where α is a simple quadratic irrational number such as 2 and 3, has been extensively studied for its arithmetic properties in various mathematical problem books, journals, and contests. This article unifies results related to such sequences over an interval that encompasses many quadratic irrational numbers, among others, as presented in Theorems 1, 2 and its corollary. We also discuss additional related topics and conclude with two open questions concerning these sequences.
Fields of Study & Subjects
Analytic Number Theory Research
Advanced Mathematical Theories and Applications
Algebraic Geometry and Number Theory
Publication details
- Journal / source
- The Mathematical Gazette
- Volume
- 110
- Issue
- 578
- Pages
- 305–317
- Publication date
- 19 January 2026
- Language
- EN