Question 112
Let $p\gt 2$ be prime. Suppose $a_1,\ldots,a_s$ are distinct elements of $\mathbb Z_p$, and $b_1,\ldots,b_s$ are also distinct elements of $\mathbb Z_p$. Prove that there is a permutation $\sigma\in S_s$ for which $a_1+b_{\sigma(1)},\ldots,a_s+b_{\sigma(s)}$ are pairwise distinct in $\mathbb Z_p$.