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I stumbled across a website by a chap called Tom Ballard in which he presents his proof of FLT based on elementary techniques: http://www.fermatproof.com

The style is rather 'non-standard', shall we say, and makes it difficult to assess. I have checked through it and have a couple of points to investigate further, but certainly the first part on pythagorean triples is interesting, and correct.

Has anybody else seen it and put in some effort to see if it is correct?

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    Voting to close. Please see this: http://meta.math.stackexchange.com/questions/2290/is-it-ok-to-ask-about-the-correctness-of-preprints-of-crank-friendly-topics. If you have any specific mathematical points you want to discuss, please post that. A blanket "is it correct?" type of question is liable to be closed.2012-02-08

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The problem is that (4) is used but not proved. (1) through (3) are merely three different versions of a definition of $r$: (1) and (2) are rearrangements of each other, and (3) is obtained from (1) or (2) by adding $z-x$ or $z-y$ to (1) or (2), respectively. So the only "Pythagorean" content is in (4). While a lot of effort is expended on showing that (1) to (3) obtain in the cubic case (which is unsurprising since they merely express the definition of $r$), (4) is just pulled out of thin air and used to claim that $x,y,z$ have to form a Pythagorean triple, when in fact (4) can only be derived by assuming that they do.

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    @Robert: He isn't projecting the case for general $n$ onto the case for $n=2$. He's projecting it into two dimensions and drawing figures that look like the ones he drew for $n=2$, but the relationship $x^2+y^2=z^2$ has no basis in this case, and the corresponding relationship involving $r$ is just introduced without any justification.2012-02-08