Quaternionic Algebra Reformulation and Proof of Fermat’s Last Theorem for All Exponents Greater than 2

This paper presents a unified, algebraic proof of Fermat’s Last Theorem (FLT) for all integer exponents n > 2, using a framework based on complexified quaternion algebra. By encoding integer triples into quaternionic expressions and analyzing their exponential and scalar norm properties, the method constructs algebraic contradictions assuming nontrivial solutions. The anti-commutative nature of quaternion basis elements eliminates cross terms, isolating scalar quantities that violate unitary exponential identities. Unlike Wiles’ proof, which relies on advanced theories of modular forms and elliptic curves, this approach is elementary, algebraically elegant, and accessible to broader audiences. It offers a conceptual alternative that is both rigorous and generalizable and may inspire further applications in hypercomplex algebra and Diophantine analysis.