Erdős Problem #267

Erdős problem #267 · erdosproblems.com/267

If $n_1 < n_2 < \cdots$ with $n_{k+1}/n_k \ge c > 1$, must $\sum_k 1/F_{n_k}$ be irrational? The proposed proof closes the range $1 < c < 2$ left open by earlier criteria.

Result

Proved

Status

Candidate (review pending)

AI contribution

AI-discovered

Method

Argument

Field

Number Theory, Irrationality

Posed by

—

Year posed

—

Years open

—

Solved

2026-07-13

Model

GPT-5.6 starships (Claude Fable 5 reviewer)

Vendor

OpenAI / Anthropic

Collaborators

—

Verification

Lean-verified

Publication

Announced

Significance

10 / 100*

Disclosed cost

—

Wikipedia

No dedicated article