English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Fermat's statement is equivalent to say that if $x$, $y$, $z$, $n$ areintegers and $n>2$, then $z^{n}\gtrless x^{n}+y^{n}$. This is proved with theaid of numbers $\lambda $'s, of the form $\lambda =z/\rho $, with $1<\rho<z$,named \emph{reversors} in the text, because their property of multiplying$z^{n-1}$ in $z^{n-1}<x^{n-1}+y^{n-1}$, not only reverses the signal but alsogives $z^{n}>x^{n}+y^{n}$ as a solution of the reversed inequality. As the$\lambda ^{\prime }s$ satisfy a compatible opposed sense system ofinequalities, the $\lambda$-set is equivalent to the points of an$\mathbb{R}^{+}$ interval. Therefore the theorem admits a noncountable infinityof proving ways, each one given by a particular value of $\lambda$.  In Corollary 1 a general relation between $y$, $x$, $z$ and $n$ is derived.Corollary 2 shows that the Diophantine equation in Fermat's statement admits nosolutions other than algebraic irrationals and the inherent complexes.  Integer triplets can be classified in seven sets, within each one theirrelation with the respective $n$ is the same as shown in Table 1.  Numerical verification with examples taken from all the mentioned seven setsgives a total agreement with the theory.

Fermat's Last Theorem admits an infinity of proving ways and two corollaries