Is Fermat's "Last Theorem" really Fermat's theorem?

Discussion in 'Number Theory' started by ter, May 15, 2022.

  1. ter

    ter

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    FLT is usually taken to be equivalent to Fermat's conjecture that a n-dimensional pseudo-cube
    can for n>2 not be split into two n-dimensional pseudo-cubes whereas according to Pythagoras'
    Theorem a square can be split into two squares. Translation of this proposition into an arithmetic
    expression obviously is a matter of analytic geometry which at the beginning of the 17th century was conceptualized by Rene Descartes and to which Fermat was an early contributor. Fermat's original
    conjecture may not actually be a number-theoretic proposition at all. Is it conceivable that the world's
    mathematics adepts are barking up the wrong truee? I have described the consequences of the
    geometric interpretation in http://terhardt.userweb.mwn.de/ter/misc/fltissues.html
     
    ter, May 15, 2022
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  2. ter

    ter

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    As far as I can see the similar threads here cited all are based on the assumption that
    FLT is a number-theoretic proposition. My point is that this fundamental assumption
    probably is wrong. The fact that Fermat's proposition can be proved to be true
    for certain exponents, e.g., n=3,5,7,11, and natural triples x, y, z of the equation
    x^n+y^n=z^n, does not imply that the proposition is specific to, and dependent on,
    the triple being natural. For instance, the equation x+y=z(x-y) is insoluble for x=y and
    natural triples x, y, z because it is insoluble for triples of any kind. Likewise, the
    Fermat equation is insoluble for n=3,4,... and natural triples if and because it is
    isoluble for rational or real triples.
     
    Last edited: May 15, 2022
    ter, May 15, 2022
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