# Video: What happens to Fermat’s last theorem modulo a prime number p?

This year in January I started finding more and more counter examples to the last theorem of Pierre de Fermat. I started in the space of 3D complex numbers using the so called divisors of zero you can find there. Rather soon after that I found those very easy to understand counter examples using modular arithmetic modulo N where N was the product of two prime numbers. Along the way I found out there is also a cute improvement to make to the so called little theorem of Fermat, that was one of the many cute results of this year. Simple example:
Take 107^2, the old little theorem of Fermat says you must take it modulo 2 and you get the number 1. With the improved little theorem you do not take it mod 2 but mod 2*107 or mod 214. And voila: 107^2 mod 214 = 107.
So the problem of the little theorem of Fermat with small exponents is more or less solved in this way. It was a cute result for sure…:)

Yet since January I have been wondering if all counter examples must use some form of divisors of zero. If so there would be a small possibility to strongly improve on the result from Andrew Wiles. The video below shows a counter example using only integers modulo a prime number p. Since those number spaces modulo p do not have divisors of zero, actually these spaces are fields, I can now say that it is not needed to have divisors of zero. So that is why I decided to include this video in this post: it saves me a lot of time and funny enough this result goes back to at least the year 1917.

Lately there are much more math video’s on the usual video channels and a lot of them have these beautiful animations. A significant part of those new video’s can be traced back to the work of the guy that runs the 3Blue1Brown channel who more or less started to craft those beautiful animations. Somewhere this summer or may be spring he called for the public to make their own math video’s and even I thought about it a short time. But I have no video editing software, I have zero experience in using such software, I have no microphone and the only video camere I have is my photo camera that I never use to make video. So I decided not to try and make a video about 3D complex numbers, it was just too much work.
Here is how the small picture from the video looks on Youtube, it looks cute but likely it takes a lot of time to make such animations:

Ok, back in the year 1917 a guy named I. Schur managed to find a counter example using the integers modulo a prime number. He himself in that old article cites another person so it is a bit vague how this all panned out. Anyway I do not have to be ashamed as not to find this result modulo p; it is based on the colorings of graphs like you see above. I do not know much about that so don’t blame me for missing these results. Besidew that, another cute result of this year was that I found out that my own 4D complex numbers form a field if you restrict them to the rational numbers. That simply disproves stupid but accepted theorems like the Hurwitz theorem that says that the only higher dimensional complex numbers are the quaternions and total garbage like the octonions. That whole fucking stupid theorem from Hurwitz is just not true and of course the mathematical community says nothing.
Anyway, the video is just 10 minutes of your time and my post is only two pictures long so have fun with it!

And now we go for the video:

The paper that was unpicked is written in German but don’t panic: It is not in that gothic font they used for a long time. You can find it here:
https://eudml.org/doc/145475.
So if you can read the German language you can try to unpick it for yourself… Ok, end of this post. Thanks for your attention.

# What happens if an electron beam hits a magnetic field? Five easy calculations around magnetism.

It is just past midnight on a Saturday so why not start this new post? Two weeks ago all of a sudden I felt like doing a magnetics post once more and to be honest that is a tiny miscalculation because this is also post number 200. This should actually be about higher dimensional complex numbers or so but it is what it is so we are doing magnetics.
This year I stopped working on the magnetic pages on the other website, after more than five years and zero response I decided to classify the physics professors the same as the math professors: Just another bunch of incompetents that you better avoid being around. That policy stays in tact so although this post is very long you should not view this as an attempt to change the views physics professors have on magnetism in particular the idea that electrons must be magnetic monopoles because all other interpretations are not logical. To be honest I feel a bit more free now, now I can say you are a total idiot or a complete moron or a natural born imbecile instead of every time trying to come up with more reasons as why electrons cannot be magnetic dipoles.
This post contains five easy calculations around magnetism, to be a bit more precise: there are three forces that can act on an electron (Coulomb, Lorentz and say the Stern-Gerlach force) and the five easy calculations cover that. Ok, gravity also works on electrons but that is out of this story.
We will look at the speed and the acceleration of electrons and we will try to estimate how much of a gradient a magnetic field must have to explain the observed experimental results. I found a gradient of about 450 million Tesla/meter and that all in my living room… I cannot find a fault in it and of course a gradient so large is not realistic so I reject the way electron potential energy related to magnetism is incorperated into the standard model of particles.
Last week I found a perfect photo that can serve as a model of how physics professors are behaving in my view (a bunch of overpaid incompetents). The ‘blah blah blah’ can serve as my five easy calculations; for the idiots and imbeciles that the physics professors are, these calculations will be ‘blah blah blah’ material. Come on, next year 2022 it will be one 100 years since the Stern-Gerlach experiment was performed. If a collection of overpaid idiots have it wrong for one 100 years, the most logical thing is that they will keep it wrong for at least another 100 years.

Excluded the picture above, this post is 14 pictures long. And even then I skipped a lot of stuff like when talking about the solar wind I just assume all particles go with the same speed of say 750 km/sec. Of course that is an oversimpification; there are many different particles in the solar wind that all behave rather different.
I hope you don’t loose oversight and therefore I would like to explain how I arrived at that crazy magnetic gradient of 450 million Tesla/meter.
Here we go:

1) I estimate how fast electrons go in an old color television where I assume these electron have a kinetic energy of 40.000 eV. This is about 120 thousand km/sec or about one third the speed of light.

2) If you place a stack of those strong neodymium magnets at the television screen you see a black spot where no electrons land. I estimate the sideway acceleration the electrons make and that is a crazy huge number: about 4.5 times 10^15 m/sec.
That might sound very huge but it is just simple Newtonian mechanics: If the electron has a sideway acceleration this big for about 2 nanoseconds, the sideway displacement is about 1 cm. That is in line with what the photo of the television screen says..

3) I calculate the force on the electron for this sideway acceleration and plug this into the expression the professional physics professors use for the force related to inhomogeneous magnetic fields and voila: there is your gradient of only 450 million Tesla/meter.

All in all the five calculations are say advanced high school level / first year university level. Given the fact that physics professors keep on thinking that electrons are tiny magnets with a north and a south pole we can safely conclude that even a science like physics is much more some kind of social construct and not a hard ball science in itself.

Enough of the introductory talk, here are the 14 pictures:

Ok, that was it for this post. Please remark that the polar aurora’s do exist for real while the blah blah blah of physics professors explaining this makes not much sense. For example they do not explain why the electrons go so fast that they ionize the air and most of all: These idiots are not aware they are missing something here.

At last I want to remark that for me it feels rather refreshing to talk about physics professors as idiots and imbeciles. That is much better as always being polite and respectful. Why should overpaid idiots and imbeciles also face a lot of completely misplaced respect?
See you in the next post & thanks for your attention because this post was a long reading for you.