The board / number theory / #239
Erdős Problem #239
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.
What the community database records, not our verdict. erdosproblems.com no longer shows statuses (why).
Let \(f:\mathbb{N}\to \{-1,1\}\) be a multiplicative function. Is it true that \[ \lim_{N\to \infty}\frac{1}{N}\sum_{n\leq N}f(n)\] always exists? The answer is yes, as proved by Wirsing [Wi67], and generalised by Halász [Ha68].
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research solved. The authoritative wording is on erdosproblems.com/239.Prizenone
Topicsnumber theory
Statement in LeanFormal Conjectures
Solution in Leanyes
Original pageerdosproblems.com/239
Attempts
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