Date: Dec 29, 2012 3:47 AM
Author: quasi
Subject: Re: request for help with lemma (algebra, summations)
Orange Pekoe wrote:

>

>Let me start by saying that the link isn?t really a lemma, but

>since it?s probably not a proof either, I didn?t know what to

>call it.

>

>I should also quickly add that I?m not a mathematician - or even

>close ? so I don?t really expect to be taken seriously. Even so,

>I hope you will take a look at the link and try to get at least

>a few lines into the equations. The whole thing is well under 2

>pages printed so this is at least guaranteed not to waste (much)

>of your time.

>

>I never use the proper name of the problem but that will be

>immediately obvious so you might want to refrain from sipping

>any beverages until you get past the first couple of paragraphs

> ? for the sake of your keyboard and monitor.

>

>I know I'm making light of this, but I am serious about wanting

>to know if I might be on to something.

Your attempt is likely worth nothing as far as the mathematics

go, however a possible value is that it may spur you on to a

more serious self-study of math in order that you may eventually

be able to recognize and construct valid proofs.

>thx

>

>http://ftgfop.blogspot.fr/

Your assumption a < b < c is innocent, but your assumption

x < y < z requires justification. It's not immediately clear

that you can get away with that.

Very suspect is your later "simplification" where you assume

a^2 + b^2 = c^2. That's effectively assuming n = 2, but the

whole point is to start with the assumption that n > 2.

Perhaps the most blatant flaw is that, as far as I can see,

you never use the assumption that a,b,c are positive integers.

I don't see any mention of divisibility or congruences or

any reasoning that would fail if a,b,c were only assumed to

be positive reals. I mean, the equation a^3 + b^3 = c^3

_does_ have solutions for a,b,c positive reals -- simply

choose a,b > 0 and let c be (a^3 + b^3)^(1/3).

Besides that, your lack of knowledge of how to express things

rigorously renders your proof mostly unreadable, so for now,

aside from the objections I made above, I won't try to decipher

it any further.

quasi