An Elementary Proof for Fermat's Last Theorem using a Transformation Equation to Fermat's Equation
Year: 2025
Type: article
Abstract: Fermat’s Last Theorem states that there are no positive integers x, y and z satisfying the equation x n + y n = z n, where n is any integer > 2. Around 1637 Fermat proved that there are non-zero solutions to the above equation with n = 4. In the 18th century Euler treated the case n = 3, thereby reducing the proof for the case of a prime exponent ≥ 5 in this proof we hypothesize that r, s and t are positive integers satisfying the equation rp + sp = tp , where p is any prime >3 and establish a contradiction. We use an Auxiliary equation x 3 + y3 = z3 and create transformation equations. Solving the transformation equations we prove that only a trivial solution exists in the main equation r p + sp = tp.
Authors: Retired Executive Engineer, Energy Conservation Cell), Tamil Nadu State Electricity Board, Anna Salai, Chennai (Tamil Nadu), India., P.N Seetharaman
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
OpenAlex ID: W4409789916