The board / irrationality / #257
Erdős Problem #257
OPENdatabase updated 2025-08-31
No proof or disproof is known, and it isn't known whether a finite computation could settle it.
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Let \(A\subseteq\mathbb{N}\) be an infinite set. Is \[ \sum_{n\in A} \frac{1}{2^n - 1} \] irrational?
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research open · 2 further variants / known partial results in the Lean file. The authoritative wording is on erdosproblems.com/257.Prizenone
Topicsirrationality
Statement in LeanFormal Conjectures
Solution in Leanno
Original pageerdosproblems.com/257
Attempts
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Live page status OPEN (0 claimed proofs), but “Currently working on this problem” lists daniel_e_ruiz_c and memeister27; mandatory no-collision stop.
SKIPPED