Erdős Problem 903

### What is the conjecture

https://www.erdosproblems.com/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 $t\geq n+p$?

Status: solved

### Choose either option
- [ ] I plan on working on this conjecture
- [x] This issue is up for grabs: I would like to see this conjecture added by somebody else

The issue names only the Erdős Problems 903 statement and no repository file or test. Read the linked conjecture first, then inspect existing formal-conjecture entries to find the appropriate Lean entry point; done means the statement is added and the project checks it.

Written by the indexing model from the issue text.