The board / number theory / #347
Erdős Problem #347
PROVED LEANdatabase updated 2026-01-21
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).
The set of subset sums of a set `A ⊆ ℕ`. -/ local notation "𝓟" A => subsetSums A /-- Is there a sequence \(A=\{a_1\leq a_2\leq \cdots\}\) of integers with \[\lim \frac{a_{n+1}}{a_n}=2\] such that \[P(A')= \left\{\sum_{n\in B}n : B\subseteq A'\textrm{ finite }\right\}\] has density \(1\) for every cofinite subsequence \(A'\) of \(A\)? This has been solved in the affirmative by ebarschkis in the comments (based on idea of Tao and van Doorn, also in the comments). This was formalized in Lean by Barschkis using Aristotle.
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research solved. The authoritative wording is on erdosproblems.com/347.Prizenone
Topicsnumber theory, complete sequences
Statement in LeanFormal Conjectures
Solution in Leanyes
Original pageerdosproblems.com/347
Attempts
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