Problem 493

Does there exist a $k$ such that every sufficiently large integer can be written in the form

\prod_{i=1}^k a_i - \sum_{i=1}^k a_i

for some integers $a_i\geq 2$ ?

Source: erdosproblems.com/493

Number theory

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An accepted solution exists. The statement is true.

PROVED (LEAN): the site's label, crediting Seamans's two-term identity. The claim page Seamans records the result and its acceptance, and Alexeev's AI-generated Lean proof of the same identity, which this repository has not built, is a pending claim.

Problem 493

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Proof claims

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