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

Marco Timpanella

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