The primary aim of this paper is to study the problem of a new fifth power mean of the two-term exponential sums. By employing elementary methods, the number of solutions to a few congruence equations is obtained. Besides certain properties of classical Gauss sums have been derived.

the two-term exponential sums, fifth power mean, elementary method, calculating formula

Received: November 27, 2024; Revised: December 15, 2024; Accepted: January 18, 2025; Published: March 7, 2025

How to cite this article: Yating Du, On two-term exponential sums and a new fifth power mean, JP Journal of Algebra, Number Theory and Applications 64(2) (2025), 199-219. https://doi.org/10.17654/0972555525012

This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License

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