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arXiv · 2507.04521

Every real number is a sum of two real numbers with diverging partial quotients

Dmitry Gayfulin·Erez Nesharim
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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.

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Dmitry Gayfulin, Erez Nesharim. 2025-07-06. Every real number is a sum of two real numbers with diverging partial quotients. https://arxiv.org/abs/2507.04521

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