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Is the set of odd integers not of the form the union of an infinite arithmetic progression and a set of density ?
Source: erdosproblems.com/16
An accepted solution exists. The statement is false.
DISPROVED (LEAN), the site's label (page last edited 05 April 2026): Chen's 2023 preprint [Ch23] shows that the odd integers not of the form are not a finite union of arithmetic progressions plus a set of density zero, so the answer is no; the site's Lean marker corresponds to the proof the formal-conjectures catalog links, Daniel Chin's Lean file, which proves that no single infinite progression plus a progression-free remainder equals that set of odd integers, a statement that implies the negative answer. The claim page Chen's disproof records the acceptance evidence: the curator of erdosproblems.com, Thomas Bloom, with no refereed publication found; the corpus has not built or audited the Lean proof.