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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FormalConjectures/ErdosProblems/

1003.lean

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Erdős, Pomerance, and Sárközy [EPS87] proved that for all large $x$ , the number of $n \leq x$ with $\phi(n) = \phi(n+1)$ is at most $\frac{x}{\exp((\log x)^{1/3})}$ .

[EPS87] Erdős, Paul and Pomerance, Carl and Sárközy, András, _On locally repeated values of certain arithmetic functions_. {II}. Proc. Amer. Math. Soc. (1987), 1--7.

FormalConjectures/ErdosProblems/1003.leanErdos1003.erdos_1003.variants.eps871 lineExact file

1∀ᶠ (x : ℝ) in Filter.atTop, ↑{n | ↑n ≤ x ∧ n.totient = (n + 1).totient}.ncard ≤ x / Real.exp (Real.log x ^ (1 / 3))

SolvedStatement only, no proof

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