The main purpose of this article is using the analytic methods and the properties of the classical Gauss sums to study the calculating problem of the hybrid power mean of the two-term exponential sums and quartic Gauss sums and then prove two interesting linear recurrence formulas. As applications, some asymptotic formulas are obtained.

中文翻译：

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二项指数和与四次高斯和的一类混合幂均值

本文的主要目的是利用经典高斯和的分析方法和性质，研究二项指数和与四次高斯和的混合幂均值的计算问题，然后证明两个有趣的线性递推公式。作为应用，获得了一些渐近公式。