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For any , let be the minimal (if it exists) such that there are with a square. Let . What is the order of growth of for ? For example, is it true that ?
Source: erdosproblems.com/374
An accepted solution exists. Settled in another form, for example when its parts resolve differently or the question is open-ended.
OPEN was the erdosproblems.com label; its discussion thread was read 2026-10-07. The derived standing, solved and answered, departs from the label. It rests on two accepted claims that reach the same conclusions, Hartley and Olson's (claim page (Hartley and Olson, 2026)) and Yudin's (claim page (Yudin, 2026)). Jacob Parish at Plasma AI checked and accepted both, and this corpus built Hartley and Olson's Lean development and audited the statements it proves, which are also the statements with which Yudin's claim answers the question. The erdosproblems.com curator has credited neither claim. The erdosproblems.com proof-claims tab carries three proof claims. Hartley and Olson and Yudin each claim the full determination. Hartley and Olson's forum submission covered the positive lower density of , and their revised paper adds the orders of growth of through . Zeraoulia's partial claim of 2026-07-27 is the bound with certified computations. It determines no order of growth and does not reach . So it settles no instance and has no claim page.