The board / number theory / #1110
Erdős Problem #1110
OPENdatabase updated 2025-12-07
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).
\(n\) is representable with respect to \(p\) and \(q\) if it is the sum of a finite divisibility antichain of terms of the form \(p^kq^l\).
Let \(p>q\geq 2\) be two coprime integers. We call \(n\) representable if it is the sum of integers of the form \(p^kq^l\), none of which divide each other. If \(\{p,q\}\neq \{2,3\}\) then what can be said about the density of non-representable numbers? Are there infinitely many coprime non-representable numbers, that is, an infinite family of pairwise coprime non-representable integers?
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research open. The authoritative wording is on erdosproblems.com/1110.Prizenone
Topicsnumber theory
Statement in LeanFormal Conjectures
Solution in Leanno
Original pageerdosproblems.com/1110
Attempts
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