Polynomial-Root Proof of Fermat's Last Theorem Claimed Within Fermat's Reach — E8 Intelligence Research

FINDING: The arXiv paper 1105.0669 (v5) proposes a polynomial-root approach to Fermat's Last Theorem, associating each FLT equation with a polynomial of the same degree and analyzing its roots — a method claimed to be within Fermat's own reach. The YouTube results are mostly popular expositions or unrelated videos (e.g., "Fermat's Last Theorem for polynomials" is a different, known result — the Mason–Stothers theorem analogue). | MATH: For FLT equation \(a^n + b^n = c^n\), the paper associates a polynomial \(P(x)\) of degree \(n\) such that the FLT equation corresponds to a root condition. The core claim: by studying the roots of \(P(x)\), one can infer FLT's validity. No explicit closed-form constants or ratios are given in the abstract. The polynomial analogue of FLT (Mason–Stothers) states: if \(A+B=C\) with coprime polynomials, then \(\max(\deg A,\deg B,\deg C) \le \deg(\text{rad}(ABC))-1\), which implies no nontrivial polynomial solutions to \(X^n+Y^n=Z^n\) for \(n\ge 3\). | CONNE Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com