Erdős Problem #906
Erdős problem #906 · erdosproblems.com/906
Is there an entire non-zero function such that, for any infinite sequence , the set is everywhere dense? The literal question is trivial for polynomials, so the claims address the transcendental entire case, in the affirmative.
- Result
- Proved(see note)
- Status
- Candidate (review pending)
- AI contribution
- AI co-developed
- Method
- Argument
- Field
- Analysis, Entire Functions
- Posed by
- Paul Erdős
- Year posed
- 1956
- Years open
- 70y
- Solved
- 2026-04-25
- Model
- GPT-5.5 Pro
- Vendor
- OpenAI
- Collaborators
- Przemysław Chojecki
- Verification
- Unreviewed
- Publication
- Announced
- Significance
- 10 / 100
- Disclosed cost
- —
- Wikipedia
- No dedicated article
What was actually shown
Two independent affirmative claims (Adriano's, posted first, and a GPT-5.5 Pro note); Erdős himself wrote in 1982 that the problem had been solved affirmatively long before, without a locatable reference
What the AI did
The probabilistic argument via the cofinite reformulation, using Sodin's Edelman-Kostlan and Offord-type estimates for Gaussian analytic functions, was developed with GPT-5.5 Pro; an independent solution by another contributor was posted first the same day.
Verification
AI screenings reported one minor issue on each claim; no formalization (the required tools are not in mathlib) and no independent expert review; erdosproblems.com still lists the problem open.