论文标题

二,三,四,五个,六个,七个,八和九的六n度功率的参数解决方案

Parametric Solution to six n degree powers for degree two, three, four, five, six , seven, eight, and nine

论文作者

Couto, Oliver, Tomita, Seiji

论文摘要

从历史上看,在数学文献中,在某些情况下,在等式的两侧,不同的作者为六个权力提供了方程1的解决方案,而不同程度为2,3,4,5,6,6,7,8,9。请参阅A. Bremner和J. Delorme和Tito Piezas的参考编号1。不同之处在于,本文对方程式1进行了系统分析。尽管方程1的数值解决方案可在Wolfram Math网站上获得,但在各个程度上搜索了方程1的参数解决方案2,2,3,4,5,6,7,8,99均未产生结果。本文的作者在等式1的每一侧都选择了六个术语,因为每次在等式1的两侧删除一个项时,问题的难度都会增加。作者为等式1提供了参数解决方案,用于2、3、4、5&6,以及使用椭圆曲线方法的7、8和9级解决方案。我们还想提到,使用椭圆曲线方法的7、8和9学位的解决方案具有无限的数值解决方案。关键字,纯数学,二元方程,相等的总和,参数方程。

Historically in math literature there are instances where solutions have been arrived at by different authors for equation 1 for six powers on both side of equation, for different degree 2,3,4,5,6,7,8,9. See reference number 1, by A. Bremner & J. Delorme and reference number 10, by Tito Piezas. The difference is that this paper has done systematic analysis of equation 1. While numerical solutions for equation 1, is available on Wolfram math website, search for parametric solutions to equation 1, in various publications for all degree 2,3,4,5,6,7,8,9 did not yield results. The authors of this paper have selected six terms on each side of equation 1, since the difficulty of the problem increases every time a term is deleted on each side of equation 1. The authors have provided parametric solutions for equation 1, for degree 2, 3, 4, 5 & 6 and for degree 7, 8 & 9 solutions using elliptical curve method has been provided. Also we would like to mention that solutions for degree 7, 8 & 9 using elliptic curve method has infinite numerical solutions. Keywords, Pure math, Diophantine equations, Equal sums, parameteric equations.

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