Abstract
Let R=GR(p2,2n) be a Galois ring and Fq a finite field, where q=p2n. In this paper, we study the number of solutions of equations of the form a1x1d1+⋯+asxsds=b with xi∈GR(p2,2ti), where ai,b∈R∖{0} and ti|n for all i=1,...,s, and employ results on quadratic forms over finite fields to give an explicit formula for the number of solutions of diagonal equations with restricted solution sets satisfying certain natural restrictions on the exponents. As a consequence, we present conditions for the existence of solutions.
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