Past exam of the mathematics course of the University of Cambridge / 2021 / iii / Paper 161 / 4 / ii / Solution

Let $\mathcal{A}$ be an independent set in the graph. Every member has size $p^2\equiv 0(\mathrm{mod}p)$, while for distinct $A,B\in \mathcal{A}$, independence means $|A\cap B|$ is nonzero modulo $p$. Apply part i withThis givesMoreover,