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Erdős problem 694

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

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FormalConjectures/ErdosProblems/

694.lean

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Carmichael has asked whether there is an integer nn for which ϕ(m)=n\phi(m) = n has exactly one solution, that is Unparsed notation: \frac{f_\max(n)}{f_\min(n)} = 1.

FormalConjectures/ErdosProblems/694.leanErdos694.erdos_694.variants.carmichael1 lineExact file
sorry ↔ ∃ n > 0, ∃! m, m.totient = n
OpenStatement only, no proof