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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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

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