Fermat Last Theorem: A proof for a special case

[mohamadh95]

Please take me seriously, I know proving Fermat last theorem is not easy but I may have just proved it for a special case, everything is in the picture, so please tell if what I did is wrong or it's okay. I may have not reached the proof but I think I was on the way, just see the picture.
Thank you for your time

 

[verty]

Please take me seriously, I know proving Fermat last theorem is not easy but I may have just proved it for a special case, everything is in the picture, so please tell if what I did is wrong or it's okay. I may have not reached the proof but I think I was on the way, just see the picture.
Thank you for your time

I see a mistake, you've written $({b \over 2})^2$ instead of ${b^2 \over 2}$.

 

[mohamadh95]

I see a mistake, you've written $({b \over 2})^2$ instead of ${b^2 \over 2}$.

Yeah you're right, I made this mistake in the figure, but I wrote ${b^2 \over 2}$ in the equations.

 

[verty]

I can't read that line after "Simplifying 3", can you write out the line just before that and the line just after that here so I can see it? At the moment it looks wholly false to me.

 

[HallsofIvy]

The fact that it is not important enough for you to type it out rather than requiring others to read poorly photographed long-hand is enough to convince me that it is not important enough for me to try to read it!

 

[Office_Shredder]

It would help a lot if you at least precisely stated what it is you are trying to prove.

EDIT: And what your manipulations are intended to do. You come up with equation 3 and then seem to simplify it all the way down to b^k = b^k. What was the point of all of that?

 

[mohamadh95]

A new decent version

I am sorry for not replying, this is a more decent version of what I was trying to show you guys. I think I got the theorem proven for any number b that is odd and where b=a+(a+n) but I don;t know how to continue when b is even.

 

[h6ss]

This proof lacks the usual standard of rigour, making it vague and hard to understand. You should be more precise about your intentions.

 

[Mark44]

Too many boxes in the illustrations
The diagram at the beginning is difficult to read. Rather than having boxes (or "callouts") with a, b, and a + n, with curved lines going over to the two vertical lines, it would be better to have two horizontal lines of equal length, with one of them divided into two parts. Put a label of b on the undivided line, and put labels of a and a + n on the divided line. No boxes, no curved lines.

The second figure is even harder to understand, due to the boxes that represent the quantities (a + n)², a², and b²/2, as well as the other boxes that clutter up the drawing.


Equation numbering
Examples such as the one shown below confused me at first.

1 - b = a + (a + n)

As shown, it looked to me like the left side was 1 - b, not b as you intended.
The usual practice when equations are numbered is to put the number after the equation, in parentheses, like this:
b = a + (a + n) (1)

I wrote the parenthesized 1 in italics so as to not be interpreted as multiplication by 1.

Also, when equations are shown with numbers, usually only the more important ones are numbered, when they are discussed later in some detail. You shouldn't number steps that aren't equations, such as when you multiply both sides by b^k-2.

 

[mohamadh95]

Thank you h6ss and Mark44 I'll try working with your advice and make the proof more "elegant" and easy to read and understand.