In this paper on FLT, one solves the case n=3 in elementary way, extensible to n odd. The author works only through the sole factorization in factors and with the proceeding for absurd, that is if x, y, z are prime among them, under the hypothesis that (x, y, z) are a solution, one obtains that the first and the second term of an equivalent relation are odd (the first) and even (the second).
Bulletin of Mathematical Sciences and Applications (Volume 2)
N. Fragnito "The Last Theorem of Fermat for n=3", Bulletin of Mathematical Sciences and Applications, Vol. 2, pp. 68-79, 2012