Erdős problem 1003 · problems.science

Are there infinitely many solutions to $\phi(n) = \phi(n+1)$ , where $\phi$ is the Euler totient function?

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3 retained statements2415f78e850a

FormalConjectures/ErdosProblems/

1003.lean

Retained formal statement3 of 3

Erdős [Er85e] says that, presumably, for every $k \geq 1$ the equation $\phi(n) = \phi(n+1) = \cdots = \phi (n+k)$ has infinitely many solutions.

[Er85e] Erdős, P., _Some problems and results in number theory_. Number theory and combinatorics. Japan 1984 (Tokyo, Okayama and Kyoto, 1984) (1985), 65-87.

FormalConjectures/ErdosProblems/1003.leanErdos1003.erdos_1003.variants.Icc1 lineExact file

1True ↔ ∀ k ≥ 1, {n | ∀ i ∈ Set.Icc 1 k, n.totient = (n + i).totient}.Infinite

OpenStatement only, no proof

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