A new method for solving the equation $x^d+(x+1{)}^d=b$ in ${\mathbb{F}}_{q^4}$ where $d=q^3+q^2+q-1$

Liqin Qian, Minjia Shi, Wei Lu

In this paper, we give a new method answer to a recent conjecture proposed by Budaghyan, Calderini, Carlet, Davidova and Kaleyski about the equation $x^d+(x+1{)}^d=b$ in $\mathbb{F}_…