Erdős Problem #1117
OPENdatabase updated 2025-12-29
No proof or disproof is known, and it isn't known whether a finite computation could settle it.
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A July 2026 preprint strengthens the known affirmative limsup result to a finite-order class-B entire function. Separately, a polynomial whose nonzero exponents span d-m has at most d-m maximum-modulus points on every circle, sharply. The liminf question remains open.
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