Published April 30, 2025 | Version CC-BY-NC-ND 4.0
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An Elementary Proof for Fermat's Last Theorem using Three Distinct Odd Primes F, E and R

Authors/Creators

  • 1. Retired Executive Engineer, Energy Conservation Cell), Tamil Nadu State Electricity Board, Anna Salai, Chennai (Tamil Nadu), India.

Description

Abstract: In number theory, Fermat’s Last Theorem states that no three positive integers a, b and c satisfy the equation a n + b n = c n where n is any integer > 2. Fermat and Euler had already proved that there are no integral solutions to the equations x 3 + y3 = z3 and x4 + y4 = z4 . Hence it would suffice to prove the theorem for the index n = p, where p is any prime > 3. In this proof, we have hypothesized that r, s and t are positive integers in the equation r p + sp = tp where p is any prime >3 and prove the theorem using the method of contradiction. We have used an Auxiliary equations x 3 + y3 = z3 along with the main equation rp + sp = tp , which are connected by means of transformation equation through the parameters. Solving the through transformation equations we get the result rst = 0, showing that only a trivial solution exists in the main equation.

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Additional details

Identifiers

DOI
10.54105/ijam.A1191.05010425
EISSN
2582-8932

Dates

Accepted
2025-04-15
Manuscript received on 09 February 2025 | First Revised Manuscript received on 13 February 2025 | Second Revised Manuscript received on 20 March 2025 | Manuscript Accepted on 15 April 2025 | Manuscript published on 30 April 2025.

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