TL;DR
This paper presents a parametric solution to a longstanding Diophantine problem involving three positive integers whose sum, sum of squares, and sum of cubes are all perfect squares.
Contribution
It provides the first known parametric solution to a previously unsolved problem in Diophantine equations.
Findings
Derived explicit parametric formulas for the integers.
Validated solutions satisfy all the conditions.
Advances understanding of complex Diophantine systems.
Abstract
In this paper we find a parametric solution to the hitherto unsolved problem of finding three positive integers such that their sum, the sum of their squares and the sum of their cubes are simultaneously perfect squares.
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Taxonomy
TopicsCommutative Algebra and Its Applications · Algebraic Geometry and Number Theory · Advanced Mathematical Theories and Applications