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.

翻译：本文针对 Budaghyan、Calderini、Carlet、Davidova 和 Kaleyski 近期提出的关于方程 $x^d+(x+1)^d=b$ 在 $\mathbb{F}_{q^4}$ 中的一个猜想（其中 $n$ 为正整数，$q=2^n$，$d=q^3+q^2+q-1$）给出了新解法。具体而言，我们采用不同于现有文献的方法，直接确定了该幂函数 $x^d$ 的差分谱。与文献中的方法相比，我们的方法更直接且更简洁。