The board / number theory / #358
Erdős Problem #358
PROVED LEANdatabase updated 2026-08-23
The statement as posed is true, and a proof exists. A solution has also been checked by machine, in Lean.
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Let \(A=\{a_1 < \cdots\}\) be an infinite sequence of integers. Let \(f(n)\) count the number of solutions to \[n=\sum_{u\leq i\leq v}a_i.\] Is there such an \(A\) for which \(f(n)\to \infty\) as \(n\to \infty\)? Tao [Ta26] constructed such a sequence with \(f(n) \gg \log n\) for all sufficiently large \(n\).
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/358.Prizenone
Topicsnumber theory, additive basis, primes
Statement in LeanFormal Conjectures
Solution in Leanyes
Original pageerdosproblems.com/358
Attempts
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