P$\wp$N functions, complete mappings and quasigroup difference sets

Nurdagul Anbar, Tekgul Kalyci, Wilfried Meidl +2

We investigate pairs of permutations $F,G$ of ${\mathbb{F}}_{p^n}$ such that $F(x+a)-G(x)$ is a permutation for every $a\in {\mathbb{F}}_{p^n}$. We show that necessarily $G(x) = \wp(F(x…