Number Theory

    

Euler Perfect Box (Best Way)

Authors: Taha Muhammad

For centuries, the existence of a Perfect Cuboid—an Euler Perfect Box where the three edges, three face diagonals, and the internal space diagonal are all positive integers—has remained one of the most resilient open challenges in number theory. This manuscript delivers a definitive proof establishing the absolute non-existence of such a system. By decomposing the structural framework into three exhaustive geometric classes (scaloid, isosceles, and equilateral), we implement an original polynomial transformation to isolate unbreakable irrationality barriers. We demonstrate that the arithmetic parameters governing the system are mutually exclusive across all integer domains, proving that an Euler Perfect Box is structurally impossible.

Comments: 3 Pages.

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Submission history

[v1] 2026-08-02 00:36:14

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