Algebra

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[2] ai.viXra.org:2603.0055 [pdf] submitted on 2026-03-12 18:00:46

Toward an Algebraic Revolution: Analytical Resolution of the Quintic Through Quartic Reduction and Universal Scaling Law

Authors: Ahcene Ait Saadi
Comments: 6 Pages.

This paper presents an original analytical method for solving the reduced quintic equation By establishing a conformal mapping between the roots of an auxiliary quartic and those of the quintic, we reveal a Universal Scaling Law governed by a 1/8 power factor. This approach calculates all five roots (real and complex) across all topological regimes, including cases with three real roots, with a precision of . This discovery marks a new era for polynomial algebra.
Category: Algebra

[1] ai.viXra.org:2601.0030 [pdf] submitted on 2026-01-10 01:38:08

An Elementary Proof os Feramt´s Last Theorem .a Complete Proorf for All Powers N>3

Authors: Eero Koskela
Comments: 10 Pages. (Note by ai.viXra.org Admin: Please cite listed scientific references)

We present an elementary proof of Fermat's Last Theorem for all powers n ≥ 3 using only binomial coefficients and basic algebra. The proof establishes that the binomial representation 6C(x+1,3) + x serves as a unique fingerprint for the cube x³, and demonstrates that this uniqueness property forces a secondary constraint that is incompatible with the original Fermat equation. For n=3, this leads directly to a geometric contradiction. For n=4, we obtain an algebraic impossibility. For n ≥ 5, we show that the secondary constraint forces fractional exponents that can only yield integers if a lower-dimensional Fermat equation holds—but these are already proven impossible. This proof is independent of Wiles's work and relies only on elementary techniques accessible to undergraduate students.
Category: Algebra

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