The board / number theory / #253
Erdős Problem #253
DISPROVED LEANdatabase updated 2026-08-23
The statement as posed is false. A solution has also been checked by machine, in Lean.
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The predicate that `a : ℕ → ℕ` is a strictly monotone sequence such that every infinite arithmetic progression contains infinitely many integers that are the sum of distinct \(a_i\)s.
Let \(a_1 < a_2 < \dotsc\) be an infinite sequence of positive integers such that \(\frac{a_{i+1}}{a_i} \to 1\). If every arithmetic progression contains infinitely many integers which are the sum of distinct \(a_i\) then every sufficiently large integer is the sum of distinct \(a_i\).
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research solved. The authoritative wording is on erdosproblems.com/253.Prizenone
Topicsnumber theory
Statement in LeanFormal Conjectures
Solution in Leanyes
Original pageerdosproblems.com/253
Attempts
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