Symmetric homogeneous diophantine equations of odd degree

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dc.creatorReynya, M. A.
dc.date2008-09-23
dc.date2008-09-25
dc.date.accessioned2026-07-07T10:04:52Z
dc.date.available2026-07-07T10:04:52Z
dc.descriptionWe find a parametric solution of an arbitrary symmetric homogeneous diophantine equation of 5th degree in 6 variables using two primitive solutions. We then generalize this approach to symmetric forms of any odd degree by proving the following results. (1) Every symmetric form of odd degree $n\ge 5$ in $6 \cdot 2^{n-5}$ variables has a rational parametric solution depending on $2n-8$ parameters. (2) Let $F(x_1, ..., x_N)$ be a symmetric form of odd degree $n\ge 5$ in $N=6 \cdot 2^{n-4}$ variables, and let $q$ be any rational number. Then the equation $F(x_i)=q$ has a rational parametric solution depending on $2n-6$ parameters. The latter result can be viewed as a solution of a problem of Waring type for this class of forms.
dc.identifierhttps://arxiv.org/abs/0809.3973
dc.identifierhttp://arxiv.org/abs/0809.3973
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/169835
dc.subjectNumber Theory
dc.subjectAlgebraic Geometry
dc.titleSymmetric homogeneous diophantine equations of odd degree
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