Abstract
In this paper we study the Jacobi sums over a ring of residues modulo a prime power and obtain the basic relationship between Gauss sums and Jacobi sums, which allows us to determine the absolute value of the Jacobi sums. As an application, we discuss the congruence x 1 p + … + x r p ≡ 1 (mod p 2), where p is an odd prime.
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