The board / additive combinatorics / #707
Erdős Problem #707
DISPROVED LEANdatabase updated 2025-10-21
The statement as posed is false. A solution has also been checked by machine, in Lean.
What the community database records, not our verdict. erdosproblems.com no longer shows statuses (why).
**Erdős Problem 707**: It is false that any finite Sidon set can be embedded in a perfect different set modulo some \(n\). As described in [arxiv/2510.19804], a counterexample is provided in [Ha47], see below. The proof of this has been formalized. This was formalized in Lean by Alexeev using ChatGPT.
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research solved · 5 further variants / known partial results in the Lean file. The authoritative wording is on erdosproblems.com/707.Prize$1,000
Topicsadditive combinatorics, sidon sets
Statement in LeanFormal Conjectures
Solution in Leanyes
Original pageerdosproblems.com/707
Attempts
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