Let Unparsed notation: f_\max(n) be the largest $m$ such that $\phi(m) = n$, and Unparsed notation: f_\min(n) be the smallest such $m$, where $\phi$ is Euler's totient function. Investigate Unparsed notation: \max_{n\leq x}\frac{f_\max(n)}{f_\min(n)}.

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No reviewed Result is current in Vela Mathematics Program. Retained source material is shown below.

1∀ (fmax fmin : ℕ → ℕ),2  (∀ (n : ℕ), IsGreatest (Nat.totient ⁻¹' {n}) (fmax n)) →3    (∀ (n : ℕ), IsLeast (Nat.totient ⁻¹' {n}) (fmin n)) →4      ∃ o,5        Filter.Tendsto o Filter.atTop (nhds 0) ∧6          ∀ (x : ℕ),7            sSup {x_1 | ∃ n, ∃ (_ : n ≤ x) (_ : ∃ m, m.totient = n), ↑(fmax n) / ↑(fmin n) = x_1} =8              (Real.exp Real.eulerMascheroniConstant + o x) * Real.log (Real.log ↑x)

Reported activity

Reported by these sources. Not reviewed here.

• Formalization

  Erdős AI contributions wiki · 3 May-5 Jun, 2026

  Machine

  Aristotle, Claude Code, Claude Opus 4.7, GPT-5.5 Pro

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• AI standalone

  Erdős AI contributions wiki · 1 May, 2026

  Machine

  GPT-5.5 Pro

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• argument

  VibeMathed

  Machine

  GPT-5.5 Pro

  Reported outcome

  resolved

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