The board / irrationality / #266
Erdős Problem #266
DISPROVED LEANdatabase updated 2026-08-23
The statement as posed is false. A solution has also been checked by machine, in Lean.
What the community database records, not our verdict. erdosproblems.com no longer shows statuses (why).
Let \(a_n\) be an infinite sequence of positive integers such that \(\sum \frac{1}{a_n}\) converges. There exists some integer \(t \ge 1\) such that \(\sum \frac{1}{a_n + t}\) is irrational. This was disproven by Kovač and Tao in [KoTa24]. [KoTa24] Kovač, V. and Tao T., On several irrationality problems for Ahmes series. [arXiv:2406.17593](https://arxiv.org/abs/2406.17593) (2024).
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research solved · 1 further variant / known partial result in the Lean file. The authoritative wording is on erdosproblems.com/266.Prizenone
Topicsirrationality
Statement in LeanFormal Conjectures
Solution in Leanyes
Original pageerdosproblems.com/266
Attempts
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