PROVED (LEAN)
This has been solved in the affirmative and the proof verified in Lean.
Let $(S_n)_{n\geq 1}$ be a sequence of sets of complex numbers, none of which have a finite limit point. Does there exist an entire transcendental function $f(z)$ such that, for all $n\geq 1$, there exists some $k_n\geq 0$ such that\[f^{(k_n)}(z) = 0\textrm{ for all }z\in S_n?\]
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Formalised statement?
Yes
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The results on this problem could be formalisable
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Additional thanks to: AlphaProof and team, Zachary Chase, and Terence Tao
When referring to this problem, please use the original sources of Erdős. If you wish to acknowledge this website, the recommended citation format is:
T. F. Bloom, Erdős Problem #229, https://www.erdosproblems.com/229, accessed 2026-04-11
