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Problem 586
Is there a covering system such that no two of the moduli divide each other?
Source: erdosproblems.com/586
- Number theory
- Covering systems
Status
Solved, DisprovedAn accepted solution exists. The statement is false.
Disproved. The status-defining source is Theorem 1.2 of Balister, Bollobás, Morris, Sahasrabudhe and Tiba (Invent. Math. 228 (2022), 377--414, refereed): every finite covering system with moduli above has two moduli with one dividing the other, so the answer is no; the claim page is Balister, Bollobás, Morris, Sahasrabudhe and Tiba (accepted on the refereed publication and the site's credit).