The board / number theory / #31
Erdős Problem #31
PROVED LEANdatabase updated 2025-11-24
The statement as posed is true, and a proof exists. A solution has also been checked by machine, in Lean.
What the community database records, not our verdict. erdosproblems.com no longer shows statuses (why).
Given any infinite set \(A\subset \mathbb{N}\) there is a set \(B\) of density \(0\) such that \(A+B\) contains all except finitely many integers. Conjectured by Erdős and Straus. Proved by Lorentz [Lo54].
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research solved. The authoritative wording is on erdosproblems.com/31.Prizenone
Topicsnumber theory, additive basis
Statement in LeanFormal Conjectures
Solution in Leanyes
Original pageerdosproblems.com/31
Attempts
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