Why n=2 is Unique: A Structural Explanation of Fermat's Last Theorem

T This paper presents a structural explanation of why n=2 is the unique exponent admitting non-trivial solutions to Fermat's equation aⁿ + bⁿ = cⁿ, grounded in three complementary perspectives. The first is arithmetic: 2 is the unique positive integer satisfying n²=2n — the sole fixed point where additive and multiplicative arithmetic coincide. Six independent structural observations are shown to be expressions of this single identity. The second is geometric: Fermat's Last Theorem is fundamenta