The board / number theory / #346
Erdős Problem #346
SOLVEDdatabase updated 2025-08-31
Resolved in some way other than a straight proof or disproof — usual for open-ended questions, or for multi-part problems whose parts went different ways.
What the community database records, not our verdict. erdosproblems.com no longer shows statuses (why).
Is it true that for every lacunary, strongly complete sequence `A` that is not complete whenever infinitely many terms are removed from it, `lim A (n + 1) / A n = (1 + √5) / 2`? The answer is no. A counterexample recorded at [erdosproblems.com/346] has all successive ratios at least `6 / 5`, but has subsequences of successive ratios tending to two different limits, `(1 + √5) / 2` and `(1 + √5) / 2 + 1 / 4`.
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research solved · 4 further variants / known partial results in the Lean file. The authoritative wording is on erdosproblems.com/346.Prizenone
Topicsnumber theory, complete sequences
Statement in LeanFormal Conjectures
Solution in Leanno
Original pageerdosproblems.com/346
Attempts
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Live page status OPEN; it lists 1 claimed proof (a full proof/counterexample claimed by Liam Price, submitted 2026-07-15) and a current worker (SkyYang), so the mandatory no-duplication/no-collision r
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