设p为奇素数,n,k为满足n/e为奇数的正整数,其中e=gcd(n,k).文章研究一类幂函数在F_(p~n)上的差分谱,其指数d满足同余方程d(p~k+1)≡2(mod p~n-1).这类指数将Sung-Tai Choi等人(2013)研究的幂函数所对应的两类指数进行了统一和推广. Let p be an odd prime number and n and k be positive integers satisfying n / e as odd numbers, where e = gcd (n, k). The paper investigates the difference spectrum of a power function on F_ (p ~ n) d satisfies the congruence equation d (p ~ k + 1) ≡2 (mod p ~ n-1). Such indices unify the two types of indices corresponding to the power functions studied by Sung-Tai Choi et al. And promotion.