The board / irrationality / #1049
Erdős Problem #1049
OPENdatabase updated 2025-09-28
No proof or disproof is known, and it isn't known whether a finite computation could settle it.
What the community database records, not our verdict. erdosproblems.com no longer shows statuses (why).
Let \(t>1\) be a rational number. Is \(\sum_{n=1}^\infty\frac{1}{t^n-1}=\sum_{n=1}^\infty \frac{\tau(n)}{t^n}\) irrational, where \(\tau(n)\) counts the divisors of \(n\)? A conjecture of Chowla.
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research open · 1 further variant / known partial result in the Lean file. The authoritative wording is on erdosproblems.com/1049.Prizenone
Topicsirrationality
Statement in LeanFormal Conjectures
Solution in Leanno
Original pageerdosproblems.com/1049
Attempts
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The authoritative live page is OPEN with 0 claimed proofs, but lists Hotdingus as currently working on problem #1049, so the required no-collision rule applies.
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