On two conjectures about permutation trinomials over [formula omitted

Abstract

Permutation polynomials with a few terms attract researchers' interest in recent years due to their simple algebraic form and some additional extraordinary properties. In this paper, by analyzing the quadratic factors of a fifth-degree polynomial and a seventh-degree polynomial over the finite field F32k, two conjectures on permutation trinomials over F32k proposed recently by Li, Qu, Li and Fu are settled, where k is a positive integer.