The board / number theory / #586
Erdős Problem #586
DISPROVEDdatabase updated 2025-08-31
The statement as posed is false.
What the community database records, not our verdict. erdosproblems.com no longer shows statuses (why).
Is there a covering system such that no two of the moduli divide each other? Asked by Schinzel, motivated by a question of Erdős and Selfridge (see [7](https://www.erdosproblems.com/7)). The answer is no, as proved by Balister, Bollobás, Morris, Sahasrabudhe, and Tiba [BBMST22]. The moduli of a `CoveringSystem ℤ` are the ideals \((m_i)\); the modulus \(m_i\) divides \(m_j\) exactly when \((m_j)\subseteq (m_i)\).
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research solved. The authoritative wording is on erdosproblems.com/586.Prizenone
Topicsnumber theory, covering systems
Statement in LeanFormal Conjectures
Solution in Leanno
Original pageerdosproblems.com/586
Attempts
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