Year: 2025
Type: article
Abstract: In 1974, M. B. Nathanson proved that every irrational number α represented by a simple continued fraction with infinitely many elements greater than or equal to k, is approximable by an infinite number of rational numbers p/q satisfying | α − p / q | < 1 / ( k 2 + 4 q 2 ) . $|\alpha-p/q|<1/(\sqrt{k^2+4}q^2).$ In this paper, we refine this result.
Source: Mathematica Slovaca
DOI: 10.1515/ms-2025-0002
Authors: Jaroslav Hančl, Tho Phuoc Nguyen
Institution: University of Ostrava
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4407937477