# The last theorem of Fermat does not hold for the 3D so called Gaussian integers.

On the one hand it is a pity I have to remove the previous post from the top position. Never ever I would have thought that the Voyager probes would be a big help in my quest of proving that electrons are not magnetic dipoles. Electrons are magnetic monopoles, if your local physics professor thinks otherwise why not ask you local physics professor for the experimental evidence there is for the electron magnetism dipole stuff?

On the other hand this post is about Gaussian intergers for the 3D complex and circular numbers and it is with a bit of pride that I can say we have a bunch of beautiful results because the last theorem of Fermat does not hold in these spaces.

The last theorem of Fermat is a kind of negative result, it says that it is impossible for three integers x, y and z that x^n + y^n = z^n, this for integer values of n greater than 2 of course. (For n = 2 I think most readers know it is possible because those are the Pythagoras triples.)

Anyway I succeeded into writing the number 3 as the sum of two Gaussian 3D integers that are also divisors of zero. So this pair of integers, in this post I name them A and T because they are related to the famous 3D numbers alpha and tau, are divisors of zero so as such AT = 0. As such as a denial of the Fermat theorem, an important result as posted here is that A^n + T^n = 3^n. So on the 3D complex & circular numbers this result is possible while if you use only the 2D complex plane and the real line this is not possible…
But there are plenty of spaces where the Fermat conjecture or the last theorem does not hold. A very easy to understand space is the ring of integers modulo 15. In this ring there are numbers that do not have a multiplicative inverse, say 3 and 5. And if inside this ring you multiply 3 and 5 you get 15 and 15 = 0 in this ring… Hence inside this ring we have that 8^n = 3^n + 5^n (mod 15) also contradicting the Fermat stuff.

I did some internet searches like ‘Fermat last theorem and divisors of zero’ but weirdly enough nothing popped up. That was weird because I view the depth of the math results related to this divisor of zero as the depth of a bird bath. It is not a deep result or so, just a few centimeters deep. But sometimes just a few centimeters can bring a human mind into another world. For example a long time ago when I still was as green as grass back in the year 1986 I came across the next excercise: Calulate the rest of 103 raised to 103 and divided by 13. I was puzzled, after all 103^103 is a giant number so how can you find the rest after dividing it by 13? But if you give that cute problem a second thought, after all that is also bird bath deep because you can solve it with your human brain…

This post is 11 pictures long, all of the standard size of 550×775 pixels. Because I could not find anything useful about the last Fermat theorem combined with divisors of zero I included a small addendum so all in all this post is 12 pictures long.

After so much Gaussian integer stuff, there is only one addendum about the integers modulo 30. In that ring you can also find some contradictions to the standard way of presenting the last theorem of Fermat.

Ok, if you are still fresh after all that modulo 30 stuff, for reasons of trying to paint an overall picture let me show you a relatively good video on the Kummer stuff. Interesting in this video is that Kummer used the words `Ideal numbers´ and at present stuff like that is known as an ideal. For myself speaking I never use the word ´ideal´ for me these are ´multiplicative attractors´ because if a number of such an ideal multiplies a number outside that ideal, the result is always inside that ideal. Here is a relatively good video:

And now you are at the end of this post. Till updates.

# Voyager probe says: Solar electrons accelerated to 670 times the initial speed…

In the first place I wish you all a happy new year & let’s hope for some improvement this year when it comes to the new corona virus.

It seems that the Voyager probes, who are now in interstellar space, have done a remarkable discovery when it comes to electron speeds coming from the sun. This was found when observing electron bursts that originate from solar bursts, first the electrons are detected while the plasma shock wave itself only arrived weeks later. This is a happy finding because it now is very hard to deny electrons get accelerated by magnetic fields because they are all magnetic monopoles. Of course 100% of the university people will deny that electrons are magnetic monopoles, this is a clear case of the law of conservation of retardness…;)
Anyway let me post a few quotes, the first quotes come from space.com. Here is a link: https://www.space.com/nasa-voyager-electron-bursts-interstellar-space. My comment is in a bold font.

The Voyager mission has detected a new type of “electron burst,” which will provide insights into the mechanisms of flaring stars, a new study reports.

“The idea that shock waves accelerate particles is not new,” corresponding author Don Gurnett, professor emeritus in physics and astronomy at the University of Iowa,
said in a statement.

“Physicists believe these electrons in the interstellar medium are reflected off of a strengthened magnetic field at the edge of the shock wave, and subsequently accelerated by the motion of the shock wave,” the University of Iowa said in the same release. “The reflected electrons then spiral along interstellar magnetic field lines, gaining speed as the distance between them and the shock increases.”

Comment: The above is retarded nonsense that shows university people think that electrons cannot be accelerated by magnetic fields and as such you get all that blah blah blah about shockwaves that can accelerate particles. If memory serves these are Alvén waves, but it is straight in your face: 670 times as fast and that is far out of the realm any Alvén wave can do.

Since it is a joyful day, why not include some fictional pictures representing what likely is one of the Voyager probes in space:

From a website under the name extremetech.com I found the next cute quote. A CME is a solar coronal mass ejection while the ISM is the inter stellar medium:

Each time one of these big CMEs reaches the ISM, the researchers have noted an electron burst in advance — the shockwave itself didn’t arrive until 13 to 30 days after the high-energy cosmic ray electrons. It’s counterintuitive to see this signal showing up ahead of the shockwave, but the team says this is all thanks to the properties of magnetic field lines in the ionized gas of the ISM, which are apparently almost perfectly straight. Large CMEs punch through the heliopause and interact with these field lines, causing some of the electrons inside to accelerate along the magnetic straightaways. They can reach relativistic speeds, about 670 times faster than the shockwave that originally delivered them to the edge of the solar system. That’s why Voyager 1 and 2 see the electron burst before the CME shockwave.
Scientists have never seen electrons accelerated ahead of a shockwave like this. It’s an entirely new mechanism and one that could help us better understand the ISM.

Comment: Just another example of how retarded all those explanations are. It has nothing to do with the ISM but only with electrons getting accelerated by magnetic fields because electrons are magnetic monopoles. It serves as another example of a law from the social sciences namely the conservation of retardness inside academic organizations.