Furthur developements regarding Euler equation xyz(x+y+z)=a
Seiji Tomita, Oliver Couto
TL;DR
This paper derives elementary parametric solutions for Euler's equation xyz(x+y+z)=a and proves the existence of infinitely many solutions within these families.
Contribution
It provides a new elementary derivation of parametric solutions and establishes their infinite abundance for Euler's and Elkies's equations.
Findings
Derived elementary parametric solutions for the equation.
Proved infinitely many solutions exist within these parametric families.
Enhanced understanding of the solution space for Euler's equation.
Abstract
In this paper, we derived the parametric solution of Euler and Elkies, xyz(x+y+z) = a, in an elementary manner. In addition we proved there are infinitely many parametric solutions of Euler's and Elkies's family of solutions.
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Taxonomy
TopicsAdvanced Differential Equations and Dynamical Systems · Historical Geography and Cartography · Mathematics and Applications