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Is the sum
irrational?
Source: erdosproblems.com/259
An accepted solution exists. The statement is true.
PROVED (LEAN). The site labels the problem PROVED (LEAN) (page last edited 19 October 2025; accessed 2026-09-04 and 2026-10-07) and credits Chen and Ruzsa [ChRu99] with the proof of the stronger conjecture that every infinite subseries over squarefree numbers is irrational; the frontmatter standing derives from the claim page (Chen–Ruzsa, 1999) for that refereed paper. The Lean qualifier is a third-party formalization of the paper's argument that formal-conjectures cites, described under Formalization; this corpus has not built or audited it.