Every real number is a sum of two real numbers with diverging partial quotients
Number Theory
2025-07-08 v1
Abstract
We show that every irrational number is a sum of two real numbers with diverging partial quotients. The proof is constructive. The key towards these results is an algorithm which was recently developed by Nikita Shulga, and our study of this algorithm is of independent interest.
Cite
@article{arxiv.2507.04521,
title = {Every real number is a sum of two real numbers with diverging partial quotients},
author = {Dmitry Gayfulin and Erez Nesharim},
journal= {arXiv preprint arXiv:2507.04521},
year = {2025}
}
Comments
18 pages