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March 2018 Representation of a rational number as a sum of ninth or higher odd powers
M.A Reynya
Funct. Approx. Comment. Math. 58(1): 79-87 (March 2018). DOI: 10.7169/facm/1646

Abstract

In the present paper, we substantially generalize one of the results obtained in our earlier paper [RM]. We present a solution of a problem of Waring type: if $F(x_1, \dots ,x_N)$ is a~symmetric form of odd degree $n\ge 9$ in $N=16\cdot 2^{n-9}$ variables, then for any $q\in \mathbb{Q}$, $q\neq 0$, the equation $F(x_i)=q$ has rational parametric solutions, that depend on $n-8$ parameters.

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M.A Reynya. "Representation of a rational number as a sum of ninth or higher odd powers." Funct. Approx. Comment. Math. 58 (1) 79 - 87, March 2018. https://doi.org/10.7169/facm/1646

Information

Published: March 2018
First available in Project Euclid: 5 May 2017

zbMATH: 06924917
MathSciNet: MR3780035
Digital Object Identifier: 10.7169/facm/1646

Subjects:
Primary: 11D72
Secondary: 11P05

Rights: Copyright © 2018 Adam Mickiewicz University

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Vol.58 • No. 1 • March 2018
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