In this paper the author works only through the factorizzation in factors, with the proceeding for absurd, that is if x, y, z are prime among them, under the hypothesis that the tern of integers (x, y, z) were a solution of the equation x^{n} + y^{n} = z^{n}. Then he obtains that the first and the second term of an equivalent relation are odd (the first) and even (the second). Three cases are separated: 1) n is power of 2; 2) n is odd; 3) n is product of a power of 2 for an odd number. For a better understanding also the Pythagorean set of three numbers is reported.

Periodical:

The Bulletin of Society for Mathematical Services and Standards (Volume 4)

Pages:

22-40

Citation:

N. Fragnito "The Last Theorem of Pierre de Fermat, In Elementary Way", The Bulletin of Society for Mathematical Services and Standards, Vol. 4, pp. 22-40, 2012

Online since:

December 2012

Authors:

Distribution:

Open Access

This work is licensed under a

Creative Commons Attribution 4.0 International License

References:

Nicola Fragnito . EULER BRICK,. Pioneer Journal of Algebra, Number Theory and its Applications, ISSN 2231-1831 , Vol. 2 , Issue 1 , September 2011 , pp.37-43 , available online at http: /www. pspchv. com/content_1_PJANTA_vol_2_1. html.

Nicola Fragnito . A solution of the Goldbach conjecture., JP Journal of Algebra, Number Theory and Applications, Volume 20, Number 2, 2011, pp.147-211; available online at http: /pphmj. com/journals/jpanta. htm.

Nicola Fragnito . The distribution of infinite primes of the first and second type, according to the Riemann Hypothesis, of infinite pairs of twin primes and the calculus of the finite number of the consecutive pairs of twin primes., JP Journal of Algebra, Number Theory and Applications, Volume 19, Number 1, 2010, pp.13-119.

Nicola Fragnito. A solution of Collatz conjecture., Pioneer Journal of Mathematics and Mathematical Sciences, SSN 2230-9829 , Vol. 5 , 2012 , Issue 1 , pp.23-53.

Nicola Fragnito. The last theorem of Fermat for n=3, Bulletin of Mathematical Sciences & Applications, ISSN 2278-9634 , Vol. 1 No 2 (2012) pp.78-90 , available online at http: /www. bmsa. us/admin/uploads/M2StqD. pdf.