The board / number theory / #1064
Erdős Problem #1064
PROVEDdatabase updated 2025-12-12
The statement as posed is true, and a proof exists.
What the community database records, not our verdict. erdosproblems.com no longer shows statuses (why).
Let \(ϕ(n)\) be the Euler's totient function, then the \(n\) satisfies \(ϕ(n)>ϕ(n - ϕ(n))\) have asymptotic density 1. Reference: [LuPo02] Luca, Florian and Pomerance, Carl, On some problems of {M}\polhk akowski-{S}chinzel and {E}rd\H os concerning the arithmetical functions {\(\phi\)} and {\(\sigma\)}. Colloq. Math.
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research solved · 2 further variants / known partial results in the Lean file. The authoritative wording is on erdosproblems.com/1064.Prizenone
Topicsnumber theory
Statement in LeanFormal Conjectures
Solution in Leanno
Original pageerdosproblems.com/1064
Attempts
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