Erdős problem 1004
For any fixed c > 0, if x is sufficiently large then there exists n ≤ x such that the values of φ(n+k) are all distinct for 1 ≤ k ≤ (log x)^c. This is an open problem.
Sources
FormalConjectures/ErdosProblems/
1004.lean
Retained formal statement
For any fixed c > 0, if x is sufficiently large then there exists n ≤ x such that the values of φ(n+k) are all distinct for 1 ≤ k ≤ (log x)^c. This is an open problem.
True ↔ ∀ c > 0, ∀ᶠ (x : ℕ) in Filter.atTop, ∃ n ≤ x, Erdos1004.IsDistinctTotientRun n ⌊Real.log ↑x ^ c⌋₊OpenStatement only, no proof