Yicheng Pan · 潘奕成 · zoahdev

Erdős Problem 883: first-question all-n proof

埃尔德什第 883 题:潘奕成的第一问全 n 证明与 Lean 形式化

Yicheng Pan (潘奕成, zoahdev): all-n completion and Lean formalization of the first question of Erdős Problem 883, building on Donald Della Pietra's asymptotic work.

Who is the author of this contribution?

Yicheng Pan (潘奕成), whose GitHub account is zoahdev and Erdős Problems account is yichengpan, is the author of the linked all-n first-question contribution. The public proof repository contains the manuscript, Lean source, rebuild audit and reproduction errata.

这项贡献的作者是潘奕成(Yicheng Pan),GitHub 账号为 zoahdev,题目网站账号为 yichengpan。贡献范围为 Erdős #883 第一问对所有自然数 n 的完成及 Lean 形式化,建立在 Donald Della Pietra 的充分大 n 结果及核心构造之上。

Exact mathematical statement

For every natural number n and every A ⊆ {1,…,n} with |A| > floor(n/2) + floor(n/3) − floor(n/6), the induced coprime graph G(A) contains a simple cycle of every odd length ℓ satisfying 3 ≤ ℓ ≤ floor(n/3) + 1.

The repository splits the proof into exact finite certificates for n < 200000 and an analytic argument for n ≥ 200000. Its final theorem is Erdos883Verified.erdos883_firstQuestion.

Contribution, prior work and review status

Donald Della Pietra's preceding asymptotic framework and core construction are explicitly credited. This contribution completes the all-n first-question statement; it does not claim to originate that asymptotic method. The second question was previously solved by Sárközy and is outside this contribution.

The author submitted a public proof claim on 5 October 2026. Listing a proof claim does not constitute the site's verification or endorsement. The repository reports a separate source rebuild of 6,831 local Lean modules and a canonical statement check. This page summarizes those published records; it does not report a new independent rebuild.

AI tools substantially assisted the work. No independent human expert review, worldwide first priority, expert endorsement or journal acceptance is claimed.

公开提交和 Lean 内核复现记录与独立专家评审属于不同证据。本站保留前人贡献、AI 协助及尚无专家认可的披露;不把整道 #883 的所有结果归于单一作者。

Primary sources and reproducible materials