Representations of a rational number as a sum of odd powers

Abstract

In this paper, we substantially generalize one of the results obtained in our earlier paper [M. A. Reynya, Symmetric homogeneous Diophantine equations of odd degree, Int. J. Number Theory 28 (2013) 867–879]. We present a solution to a problem of Waring type: if [Formula: see text] is a symmetric form of odd degree [Formula: see text] in [Formula: see text] variables, then for any [Formula: see text], [Formula: see text], the equation [Formula: see text] has rational parametric solutions, that depend on [Formula: see text] parameters.