Erdős Problem #519
PROVED LEANdatabase updated 2026-04-19
The statement as posed is true, and a proof exists. A solution has also been checked by machine, in Lean.
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The \(k\)th power sum of a finite sequence of complex numbers.
Let \(z_1,\ldots,z_n\in \mathbb{C}\) with \(z_1=1\). Must there exist an absolute constant \(c>0\) such that \[ \max_{1\leq k\leq n}\left\lvert \sum_{i}z_i^k\right\rvert>c? \] Atkinson proved that \(c=1/6\) suffices.
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research solved. The authoritative wording is on erdosproblems.com/519.Prizenone
Topicsanalysis
Statement in LeanFormal Conjectures
Solution in Leanyes
Original pageerdosproblems.com/519
Attempts
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