The board / number theory / #868
Erdős Problem #868
SOLVED LEANdatabase updated 2026-08-23
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. 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 number of ways in which a natural `n` can be written as the sum of `o` members of the set `A`. Representations are counted as nondecreasing tuples, so that two representations differing only in the order of their summands are counted once.
Let \(A\) be an additive basis of order \(2\), let \(f(n)\) denote the number of ways in which \(n\) can be written as the sum of two elements from \(A\). If \(f(n) \to \infty\) as \(n \to \infty\), then must \(A\) contain a minimal additive basis of order \(2\)? Larsen and Larsen [LaLa26] answered this in the negative.
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research solved · 3 further variants / known partial results in the Lean file. The authoritative wording is on erdosproblems.com/868.Prizenone
Topicsnumber theory, additive basis
Statement in LeanFormal Conjectures
Solution in Leanyes
Original pageerdosproblems.com/868
Attempts
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