The board / combinatorics / #903
Erdős Problem #903
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).
Let \(n=p^2+p+1\) for some prime power \(p\), and let \(A_1,\ldots,A_t\subseteq \{1,\ldots,n\}\) be a block design (so that every pair \(x,y\in \{1,\ldots,n\}\) is contained in exactly one \(A_i\)). Is it true that if \(t>n\) then \(t\geq n+p\)? This is true, and was proved by Erdős, Fowler, Sós, and Wilson [EFSW85].
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research solved. The authoritative wording is on erdosproblems.com/903.Prizenone
Topicscombinatorics
Statement in LeanFormal Conjectures
Solution in Leanno
Original pageerdosproblems.com/903
Attempts
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