Problem 435

Let $n\in\mathbb{N}$ with $n\neq p^k$ for any prime $p$ and $k\geq 0$ . What is the largest integer not of the form

\sum_{1\leq i<n}c_i\binom{n}{i}

where the $c_i\geq 0$ are integers?

Source: erdosproblems.com/435

Number theory

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SolvedAnswered

An accepted solution exists. Settled in another form, for example when its parts resolve differently or the question is open-ended.

Solved; the site labels the problem PROVED (LEAN). The site's commentary credits Hwang and Song with the first proof, and the frontmatter standing is derived from the accepted claim page Hwang and Song's formula, accepted on the site's credit; the formula was found independently in the site's forum by Peake and Cambie, whose posts are recorded on that page and, as forum comments, have no page of their own. The Lean part of the label refers to a formalization of Cambie's forum proof, linked from the same page, which this corpus has not built or audited.

Problem 435

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Proof claims

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