The board / number theory / #1188
Erdős Problem #1188
OPENdatabase updated 2026-04-04
No proof or disproof is known, and it isn't known whether a finite computation could settle it.
What the community database records, not our verdict. erdosproblems.com no longer shows statuses (why).
A congruence class `(n, a)` represents `a (mod n)`.
The modulus is `> 1` and the residue is reduced.
`z` lies in the class `(n, a)`.
Call a set of distinct integers \(1<n_1<\cdots<n_k\) with associated congruence classes \(a_i\pmod{n_i}\) a distinct covering system if every integer satisfies at least one of these congruences. A minimal distinct covering system is one such that no proper subset forms a covering system. Let \(F(x)\) count the number of minimal distinct covering systems with all moduli in \([1,x]\). Estimate \(F(x)\). The estimate is `log(log F(x)) / log x → 1`.
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research solved. The authoritative wording is on erdosproblems.com/1188.Prizenone
Topicsnumber theory, covering systems
Statement in LeanFormal Conjectures
Solution in Leanno
Original pageerdosproblems.com/1188
Attempts
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The live page status is OPEN, but it lists one claimed proof—a full proof claimed by Colin Snyder (submitted 2026-07-15)—and “Currently working on this problem” is None, so the task’s mandatory collis
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