Number Theory

An Algebraic Field Parity Analysis of A°n + B^n = C^n Via Parameterized Law of Cosines Modifiers

Authors: Yaakov Abdelhak

We investigate the integer solutions of the Diophantine relation = for non- square integers when n> 2. By projecting parameters and as the functional side lengths of a variable geometric boundary, we leverage the Law of Cosines (LOC) to track rational and irrational distributions. Using the integer constraints inherent to Fermat's hypothesis, we demonstrate a structural field mismatch under acute angular transformations, bypassing perfect square integers handled via classical infinite descent.

Comments: 3 Pages.

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Submission history

[v1] 2026-07-26 22:54:26

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