This paper presents a proof of Fermat's Last Theorem using elementary number theory. For consecutive integer triples (a, a+1, a+2), we calculate aⁿ + (a+1)ⁿ − (a+2)ⁿ across values of a and n. The resulting table demonstrates that this difference equals zero at exactly one integer point: a=3, n=2. For all n>2, the zero-crossing falls between integers, and the difference accelerates away. Since integers are fixed points on the number line, no solution exists for n>2.