Question 35
Find all natural numbers $n$ for which there exists a permutation $(p_1,p_2,\ldots,p_n)$ of $(1,2,\ldots,n)$ such that both sets $\{p_i+i\mid1\le i\le n\}$ and $\{p_i-i\mid1\le i\le n\}$ form complete residue systems modulo $n$. (Marko Đikić)