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Erdős problem 517

If f(z) = ∑ aₖzⁿₖ is an entire function (with aₖ ≠ 0 for all k) such that nₖ / k → ∞, is it true that f assumes every value infinitely often?

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The source's own material, retained exactly.

2 retained statements36c6d0fef71a

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FormalConjectures/ErdosProblems/

517.lean

Retained formal statement1 of 2

If f(z) = ∑ aₖzⁿₖ is an entire function (with aₖ ≠ 0 for all k) such that nₖ / k → ∞, is it true that f assumes every value infinitely often?

FormalConjectures/ErdosProblems/517.leanErdos517.erdos_5175 linesExact file
sorry ↔  ∀ {f : ℂ → ℂ} {n : ℕ → ℕ},    HasFabryGaps n →      ∀ {a : ℕ → ℂ},        (∀ (k : ℕ), a k ≠ 0) → (∀ (z : ℂ), HasSum (fun k => a k * z ^ n k) (f z)) → ∀ (z : ℂ), {x | f x = z}.Infinite
OpenStatement only, no proof