Erdős problem 694 · problems.science

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

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3 retained statements2415f78e850a

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FormalConjectures/ErdosProblems/

694.lean

Retained formal statement2 of 3

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

FormalConjectures/ErdosProblems/694.leanErdos694.erdos_694.variants.carmichael1 lineExact file

1sorry ↔ ∃ n > 0, ∃! m, m.totient = n

OpenStatement only, no proof

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