An Alternative Elementary Proof for Fermat’s Last Theorem
P. N. Seetharaman
P.N Seetharaman, Retired Executive Engineer, Energy Conservation Cell), Tamil Nadu State Electricity Board, Chennai (Tamil Nadu), India.
Manuscript received on 29 March 2025 | First Revised Manuscript received on 02 April 2025 | Second Revised Manuscript received on 09 April 2025 | Manuscript Accepted on 15 April 2025 | Manuscript published on 30 April 2025 | PP: 11-16 | Volume-11 Issue-8, April 2025 | Retrieval Number: 100.1/ijbsac.H053411080425 | DOI: 10.35940/ijbsac.H0534.11080425
Open Access | Editorial and Publishing Policies | Cite | Zenodo | OJS | Indexing and Abstracting
© The Authors. Blue Eyes Intelligence Engineering and Sciences Publication (BEIESP). This is an open access article under the CC-BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/)
Abstract: Fermat’s Last Theorem states that the equation xn + y n = zn has no solution for x, y and z as positive integers, where n is any positive integer > 2. Taking the proofs of Fermat and Euler for the exponents n = 4 and n = 3, it would suffice to prove the theorem for the exponent n = p, where p is any prime > 3. We hypothesize that r, s and t are positive integers satisfying the equation r p + sp = tp and establish a contradiction in this proof. We include another Auxiliary equation x 3 + y3 = z3 and connect these two equations by using transformation equations. On solving the transformation equation we get rst = 0, thus proving that only a trivial solution exists in the main equation r p + sp = tp .
Keywords: Transformation Equations to two Fermat’s Equations. Mathematics Subject Classification 2010: 11A–XX.
Scope of the Article: Mathematical Analysis