Solution for Fermat's Last Theorem (original) (raw)

Solution for Fermat's last theorem [Solución al último teorema de Fermat]

Rev. Cient. General José María Córdova, 2016

Fermat’s Last Theorem (FLT), (1637), states that if n is an integer greater than 2, then it is impossible to find three natural numbers x, y and z where such equality is met being (x,y)>0 in xn+yn=zn. This paper shows the methodology to prove Fermat’s Last Theorem using Reduction ad absurdum, the Pythagorean Theorem and the property of similar triangles, known in the 17TH century, when Fermat enunciated the theorem [El último teorema de Fermat (FLT), (1637), establece que si n es un número entero mayor que 2, entonces es imposible encontrar tres números naturales x, y y z donde tal igualdad se cumple siendo (x, y)> 0 en xn + yn = zn. Este artículo muestra la metodología para probar el último teorema de Fermat utilizando la reducción ad absurdum, el teorema de Pitágoras y la propiedad de triángulos similares, conocidos en el siglo XVII, cuando Fermat enunció el teorema]

ANOTHER PROOF FOR FERMAT'S LAST THEOREM

In this paper we propose another proof for Fermat's Last Theorem (FLT). We found a simpler approach through Pythagorean Theorem, so our demonstration would be close to the times FLT was formulated. On the other hand it seems the Pythagoras' Theorem was the inspiration for FLT. It resulted one of the most difficult mathematical problem of all times, as it was considered. Pythagorean triples existence seems to support the claims of the previous phrase.

A study of Fermat's last theorem

Fermat, about 1637, stated that Itlt is impossible to separate a cube into two cubes, or a biquadrate into two biquadrates, or in general any power higher than the second into two powers of like degree; I have discovered a truly remarkable proof which (JJ this margin is too small to contain. 1t This theorem is known as Fermat's Last Theorem. This problem may be more simply stated by

Pythagorean Relation In Triangles and Fermat's Last Theorem

Journal of Applied Mathematics & Bioinformatics, 2023

This paper derives n-th Pythagorean relation from the edges of right triangle and the result be applied to other triangles as well as with the properties of binomial equations to discover the truly marvelous proof of Fermat's Last Theorem which the famous quotation French mathematician Pierre de Fermat quoted on the margin of his favorite book Diophantus' Arithmatica but the proof he never expressed. When the value of power n is equal to 2 FLT turns to Pythagorean Theorem, so the proof should be there [1]. If we can make a n-th power relation among the edges of right triangle, then by applying this to any triangle we will find our desire first step. For, nonhypotenuse integers [Appendix 6.1] general form of binomial equation is sufficient.

On a Simpler, Much More General and Truly Marvellous Proof of Fermat's Last Theorem (II)

English mathematics Professor, Sir Andrew John Wiles of the University of Cambridge finally and conclusively proved in 1995 Fermat's Last Theorem} which had for 358 years notoriously resisted all efforts to prove it. Sir Professor Andrew Wiles's proof employs very advanced mathematical tools and methods that were not at all available in the known World during Fermat's days. Given that Fermat claimed to have had the `truly marvellous' proof, this fact that the proof only came after 358 years of repeated failures by many notable mathematicians and that the proof came from mathematical tools and methods which are far ahead of Fermat's time, this has led many to doubt that Fermat actually did possess the `truly marvellous' proof which he claimed to have had. In this short reading, via elementary arithmetic methods which make use of Pythagoras theorem, we demonstrate conclusively that Fermat's Last Theorem actually yields to our efforts to prove it.

385 (1637-2022) years later, Fermat's proof of his last theorem has finally been rediscovered.

As is well known FERMAT reading the Commentaria in Diophantum by C. G. BACHET DE MEZIRIAC, had made a habit of annotating them in the margin. Concerning the eighth Diophantum problem, which requis1es and gives the resolution in rational numbers of the equation x^2 + y^2 = a^2, FERMAT postulate : <<On the contrary, it is impossible to divide a cube into the sum of two cubes, a fourth power into two fourth powers, and, in general, any power of degree greater than two, into two powers of the same degree.

A Deeper Analysis on a Generalization of Fermat´s Last Theorem

Journal of Mathematics Research, 2018

In 1997, the following conjecture was considered by Mauldin as a generalization of Fermat's Last Theorem: "for X, Y, Z, 1 , 2 and 3 positive integers with 1 , 2 , 3 > 2, if 1 + 2 = 3 then X, Y, Z must have a common prime factor". The present work provides an investigation focusing in various aspects of this conjecture, exploring the problemś specificities with graphic resources and offering a complementary approach to the arguments presented in our previous paper. In fact, we recently discovered the general form of the counterexamples of this conjecture, what is explored in detail in this article. We also analyzed the domain in which the conjecture is valid, defined the situations in which it could fail and previewed some characteristics of its exceptions, in an analytical way.

Results Beyond Fermat's Last Theorem

International Journal of Mathematics Trends and Technology, 2022

In this paper, some results relating to Fermat's last theorem and beyond this theorem, have been presented. The expression of the form (+) − (−) , where , are variable positive integers and > , has been analyzed to derive some results relating to the Diophantine equation = 1 + 2 + ⋯ + , where , 1 , 2 , ⋯ , are positive integers. An attempt has been made to give a simple proof of Fermat's last theorem and further this theorem has been extended to the case of = 3 relative to the equation = 1 + 2 + ⋯ +. A result as a theorem 2.1 has been given to find the least positive integral value of in the equation = 1 + 2 + ⋯ + .

A fourteenth lecture on Fermat's Last Theorem

2007

I informed you earlier of the death of Fermat. He is still alive, and we no longer fear for his health, even though we had counted him among the dead a short time ago... Letter of Bernard Medon to Nicholas Heinsius, 1652. * This is a transcription of the author's Ribenboim Prize lecture given at the CNTA meeting in Montreal in May 2002.