An Attempted Contradiction-Based Proof of Fermat's Last Theorem via Minimality and Additive Growth Bounds

We present an elementary contradiction-based proof of Fermat’s Last Theorem:
there are no positive integers x, y, z and integer n > 2 such that x^n + y^n = z^n. Our
approach assumes the existence of a minimal counterexample and analyzes its struc-
tural properties using additive growth bounds, integer inequality estimates, and descent
arguments derived from classical number theory. By leveraging convexity, modular di-
visibility, and minimality assumptions, we demonstrate that any such solution implies
the existence of a smaller one—contradicting minimality. This contradiction resolves
Fermat’s Last Theorem without reliance on modularity or elliptic curve theory.