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Published: 2022-12-22

Proving The Fermat Last Theorem for Case q≤n

Bangka Belitung University
Fermat’s last theorem Newton Binomial proof of Fermat


Fermat's Last Theorem is a well-known classical theorem in mathematics. Andrew Willes has proven this theorem using the modular elliptic curve. However, the proposed proof is difficult for mathematicians and researchers to understand. For this reason, in this study, we provide evidence of several properties of Fermat's Last Theorem with a simple concept. We use Newton's Binomial Theorem, well-known in Fermat's time. In this study, we prove Fermat's Last Theorem for case . We also use the Newton’s Binomial theorem to verify several cases .      


  1. Wiles A, 1995 Modular Elliptic Curves and Fermat’s Last Theorem Ann. Math. 141, 3 p. 443.
  2. Cai T Chen D and Zhang Y, 2015 A New Generalization of Fermat’s Last Theorem J. Number Theory 149 p. 33–45.
  3. Ferreira J W P, 2016 Solution for Fermat ’ s Last Theorem 17 p. 418–425.
  4. Rostamian R, 2004 A Marvelous Simple Proof Of Fermat’s Last Theorem Discovered Ranber Statistics (Ber).
  5. Karmakar S B, 2020 An elementary proof of Fermat’s last theorem for all even exponents J. Math. Cryptol. 14, 1 p. 139–142.
  6. Wiles A, 2016 Fermat â€TM s Last Theorem Implied by.
  7. Sghiar M, 2018 Two simples proofs of Fermat ’ s last theorem and Beal Mohamed Sghiar To cite this version : HAL Id : hal-01918123.
  8. Mazaris A, 2018 A new proof of fermat’s last theorem Open Access J. Math. Theor. Phys. 1, 3 p. 107–113.
  9. Kaushish M, 2010 Fermat’s last theorem and unique factorization p. 1–15.
  10. VINAY K, 2018 Proof of Beal’S Conjecture and Fermat Last Theorem Using Contra Positive Method i-manager’s J. Math. 7, 2 p. 1.
  11. Romanov V N, 2018 The Method of Proof of Fermat’s Last Theorem IOSR J. Math. 14, 3 p. 1–5.
  12. de Alwis A C W L, 2016 Solutions to Beal’s Conjecture, Fermat’s Last Theorem and Riemann Hypothesis Adv. Pure Math. 6, 10 p. 638–646.
  13. Freitas N Kraus A and Siksek S, 2018 On The Asymptotic Fermat’s Last Theorem Ann. Mathématiques Blaise Pascal 1, 1 p. 1–5.
  14. Anton H and Rorres C, 2013 Elementary Linear Algebra: Applications Version, 11th Edition Wiley eGrade.
  15. Dummit D S and Foote R M, 2004 Abstract Algebra 3rd ed. John Wiley & Sons Inc.