Erdős problem 694

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)}.`

Sources

The source's own material, retained exactly.

3 retained statements36c6d0fef71a

FormalConjectures/ErdosProblems/

694.lean

Retained formal statement3 of 3

Erdős has proved that if there exists an integer $n$ for which $\phi(m) = n$ has exactly one solution, then there must be infinitely many such $n$ .

FormalConjectures/ErdosProblems/694.leanErdos694.erdos_694.variants.inf_unique1 lineExact file

1(∃ n > 0, ∃! m, m.totient = n) → {n | ∃! m, m.totient = n}.Infinite

SolvedStatement only, no proof