Erdős Problems

Browse all problems

↑ ↓ to move↵ to openesc to close

Loading problem…

Status

On this page

Status

Topics

Terms Privacy info@plasma.ai

Problem 903 — Erdős Problems

Problem 903

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 $t\geq n+p$ ?

Source: erdosproblems.com/903

Combinatorics

Wiki page

Status

Solved·, Proved

An accepted solution exists. The statement is true.

Proved. The site labels the problem PROVED (page last edited 24 October 2025).

EFSW85: Erdős, P. and Fowler, Joel C. and Sós, Vera T. and Wilson, Richard M., On $2$ -designs. J. Combin. Theory Ser. A 38 (1985), no. 2, 131--142.
dBEr48: de Bruijn, N. G. and Erdős, P., On a combinatorial problem. Nederl. Akad. Wetensch., Proc. 51 (1948), 1277--1279 = Indagationes Math. 10, 421--423.

Proof claims

Loading proof claims…

Discussion

Loading discussion…

PreviousProblem 902 NextProblem 904

On this page

Statement
Status
References
Proof claims
Discussion

Status: Solved, Proved
Topics: Combinatorics
In the wiki: Wiki page