A complete characterization of a family of permutation trinomials over ${\mathbb{F}}_{p^2}$

Marco Timpanella

Let $p>3$ be a prime and let $$f_{{\lambda }_1,{\lambda }_2}(x)=x^{p^2-p+1}+{\lambda }_1{x}^{p^2}+{\lambda }_2{x}^{2p-1}\in {\mathbb{F}}_{p^2}[x].$$ We determine all pairs $({\lambda }_1,{\lambda }_2)\in ({\mathbb{F}}_{p^2}{)}^2$ for which $f_{λ_1,…