This week the first blue berries were ripe so it is that time of the year again: Beer with blue berry juice! Lovely; it is a very smart way to get a bit of vitamins…;)

It is not much of a secret that every now and then I have some tiny forms of criticism against the professional math people. It really is minor and tiny; calling somebody an inverted asshole is often even a compliment compared to what they actually deserve. This day it is different, I came across a computer program named Pari and it is actually very good. I think or estimate this program started before we had computers with a so called GUI (=graphical user interface, you know the click stuff with a mouse). So you have to type in commando’s and press enter.

There are two versions of the program; a 32 and a 64 bit version. On my old computer the 32 version does not work properly (it does not work at all but that is more my computer to blame and not the program). The 64 bit version runs perfectly so that’s fine.

Pari seems to be used a lot by number theorists, I do not know much about number theory so that is why I never heard of the program. Pari is from France so if you speak that language will you can even install the french version of it all. For myself speaking I am glad I now finally have some program that does not limit me to the say 12 digits of a Casio hand held calculator. Not that you need so many digits very often but it is good to have that capability.

One of the other reasons for posting this is that when you do a Google search for ‘The new little theorem of Fermat’ my relevant posts from earlier this year just do not pop up on page one, two or three of the search results. On the one hand that is logical: a lot of people and websites with large traffic volumes have been writing about the little theorem of Pierre de Fermat. I would like to let it pop up a bit higher in the search results so you readers must all massively do a search every day on Google for the new little theorem of Fermat…;)

I remember that when I started this website, if I searched for 3D complex numbers you always had that stuff known as Alan’s pages (or may be Allen’s pages) popping up above me. Just always. That guy had only one page on 3D complex numbers and everything you could do wrong, Alan did it wrong. So for me it was kind of frustrating; why does that idiot pop up above me year in year out? It was only later that I realized a lot of people click on that kind of fake science because those people likely did everything wrong themselves. Likely they are professional math people who are trying to expand the complex plane to 3D space, that is something that does not work at all. If you do not base it on an imaginary unit, say* j*, with the property *j^3 = -1*, all your work will be in vain. Anyway after some time I finally popped up above that stupid Alan page and since that time it has always been higher. The lesson is you must not hurry; math is a long term thing and with this new little theorem of Pierre de Fermat it will take some time before it will be valued properly.

The Pari program is very good at doing the modulo thing, if you want to calculate *a* mod *b* in Pari you must enter the command Mod(*a, b*).

This post contains four written pictures about the new little theorem of Fermat, I left the proof out because I already wrote two proofs, after that just a few screen shots from the program Pari. And of course a few links for the downloading stuff although the Pari program is easy to find on the internet. Let me start with four pictures in the size 550×825 pixels:

This website is a WordPress website and as such it is horribly bad at handling larger image files. So I hope and pray that the screen shots that are about 850 pixels wide will display properly. Here we go, this is the opening screen of Pari and you see it is just like a DOS window:

As you see it does not display properly; it looks like it is 550 pixels wide so likely that is how I ended with those math pictures all 550 pixels wide…

A detail not to be missed is that you can get moral support and all you have to do is type the command ?17. That is very handy, so the next time you feel frustrated you do not need to go out and slaughter and kill at least 20 children and babies in order to get rid of your frustration. No, all you have to do is type ?17. It is amazing! No more baby killing, just type ?17.

Ok, next screenshot that will not display at 850 pixels wide:

In the above screen shot you see why I like this Pari computer program: You can fill in calculations like 8269^9973 for the *a* in Mod(*a, b*) and 8269*9973 for the *b* in Mod(*a, b*). Remark that 8269 to the power 9973 is a very huge number, yet Pari gives the correct answer in a split of a second.

Let’s look at the last screen shot:

In the above screen shot you see a numerical validation of the new little theorem of Pierre de Fermat. Of course we do not need such validations because I already gave two proofs for the new little theorem. But it is nice to observe that a standard computer can handle giant numbers like 8269^9973 with easy. So my compliments go to the French math community for this perfect computer program!

Here is a link to the Pari homepage: https://pari.math.u-bordeaux.fr/

Do not skip the documentation, it’s all not bad.

Ok, let me try to find that button known as ‘Publish website’ and see you around in a new post.