Research notes on every problem, and a library of the papers behind them. Built from the open erdos repository.
Updated
Claim. The full proof claim submitted to the site's proof-claim tab on 26 September 2026 by the account PingYou, which the tab credits to David Budden using the system PingYou, asserts a form stronger than the restricted statement: every positive rational number is, for every sufficiently large , the sum of the reciprocals over exactly intervals of positive integers of two or three elements, and the intervals can be required to lie beyond any prescribed bound and to be separated by any prescribed minimum gap. The case of the number answers the problem affirmatively. The claim's notes say that Lean is to follow, and the comment of 27 September 2026 under it promises the Lean development within days; no formalization link had been added on 2026-10-07. The manuscript's only link, the PDF on the submitting account's site, returned HTTP 404 on 2026-10-07, so the proof is unavailable even at the level of its statement. The claimant named on the tab is treated as the claimant; the account that submitted it is the poster.
Submission note. Posted to erdosproblems.com as a proof claim by David Budden (account PingYou) on 26 September 2026, giving "PingYou" as the AI used:
We show that every positive rational number is a sum of reciprocals over exactly k intervals of positive integers of length two or three, for every sufficiently large integer k; the intervals may be placed beyond any prescribed bound and with any prescribed minimum separation. The 1-case directly addresses this conjecture. Notes: Lean to follow
Standing. Claimed. The site's label is OPEN (page last edited 22 September 2025; accessed 2026-10-07) and the tab carries its standing notice that listing a claim implies no examination; no curator, referee or named mathematician has accepted the proof, and no refereed or arXiv version exists. The thread under the claim holds a comment of 26 September 2026 by another user observing that this is the third claimed solution after Land's and Tang's, saying they had proposed a shorter solution to both authors that they intend to write up in a few pages, and asking what this claim contributes relative to the earlier ones; the poster's reply does not answer that question and disclaims interest in credit. The shorter solution mentioned in that comment has no manuscript and no page.