Erdős Problem #494
PROVEDdatabase updated 2025-10-14
The statement as posed is true, and a proof exists.
What the community database records, not our verdict. erdosproblems.com no longer shows statuses (why).
For a finite set \(A \subset \mathbb{C}\) and \(k \ge 1\), define \(A_k\) as the multiset consisting of all sums of \(k\) distinct elements of \(A\).
A version in [Er61] by Erdős is product instead of sum, which is false. Counterexample (by Steinerberger): consider \(k = 3\) and let \(A = \{1, \zeta_6, \zeta_6^2, \zeta_6^4\}\) and \(B = \{1, \zeta_6^2, \zeta_6^3, \zeta_6^4\}\).
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · 9 further variants / known partial results in the Lean file. The authoritative wording is on erdosproblems.com/494.Prizenone
Topicsanalysis, additive combinatorics
Statement in LeanFormal Conjectures
Solution in Leanno
Original pageerdosproblems.com/494
Attempts
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