  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 $\mathbb{F}_{q^4}$, where $n$ is a positive integer, $q=2^n$
and $d=q^3+q^2+q-1$. In particular, we directly determine the differential
spectrum of this power function $x^d$ using methods different from those in the
literature. Compared with the methods in the literature, our method is more
direct and simple.
