Abstract

The main purpose of this article is using the elementary methods and the quadratic residual transformation technique, and the properties of the solutions of the congruence equations modulo an odd prime p to study the calculating problem of the eighth power mean of the two-term exponential sums, and give an interesting calculating formula for it. At the same time, the paper also provides a new and effective method for the study of the high order power mean of the two-term exponential sums.

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