A Comprehensible Proof for Fermat’s Last Theorem
P. N. Seetharaman
P. N Seetharaman, (Retired Executive Engineer, Energy Conservation Cell), Tamil Nadu State Electricity Board, Tamil Nadu, India.
Manuscript received on 25 February 2024 | Revised Manuscript received on 29 March 2024 | Manuscript Accepted on 15 April 2024 | Manuscript published on 30 April 2024 | PP: 29-34 | Volume-4 Issue-1, April 2024 | Retrieval Number: 100.1/ijam.A118105010425 | DOI: 10.54105/ijam.A1181.04010424
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Abstract: Fermat’s Last Theorem states that it is impossible to find positive integers A, B and C satisfying the equation An + Bn = Cn where n is any integer > 2. Taking the proofs of Fermat for the index n = 4, and Euler for n = 3, it is sufficient to prove the theorem for n = p, any prime > 3. We hypothesize that all r, s and t are non-zero integers in the equation r p + sp = tp and establish contradiction. Just for supporting the proof in the above equation, we have another equation x 3 + y3 = z3 Without loss of generality, we assert that both x and y as non-zero integers; z3 a non-zero integer; z and z2 irrational. We create transformed equations to the above two equations through parameters, into which we have incorporated the Ramanujan – Nagell equation. Solving the transformed equations we prove the theorem.
Keywords: Transformed Fermat’s Equations through Parameters. 2010 Mathematics Subject Classification 2010: 11A–XX.
Scope of the Article: Applied Mathematics