The board / number theory / #476
Erdős Problem #476
PROVED LEANdatabase updated 2025-12-31
The statement as posed is true, and a proof exists. A solution has also been checked by machine, in Lean.
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Let \(A\subseteq \mathbb{F}_p\). Let \[ A\hat{+}A = \{ a+b : a\neq b \in A\}. \] Is it true that \[ \lvert A\hat{+}A\rvert \geq \min(2\lvert A\rvert-3,p)? \] This is the Erdős-Heilbronn inequality, proved by Dias da Silva and Hamidoune.
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research solved. The authoritative wording is on erdosproblems.com/476.Prizenone
Statement in LeanFormal Conjectures
Solution in Leanyes
Original pageerdosproblems.com/476
Attempts
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