Youri Kraskov - The Wonders of Arithmetic from Pierre Simon de Fermat

2nd entry: The second case is impossible because the number 2aabb is not a square .

3rd entry: New solution to the Pythagorean equation AB=2Q .

4th record: It may be computed as many numbers aa+bb–cc=a+b–c as you like .

5th entry: And in general, it is impossible to decompose any power greater than 2 into two powers with the same index. Proof by a key formula method .

6th entry: However, you can calculate as many numbers C+QQ=CQ as you like .

Now this restored text in margins of book can be compared with the text published in the edition "Arithmetic" by Diophantus with Fermat’s comments in 1670 (see Pic. 3 and at the end of Pt. 4.2):

However, it is impossible to decompose a cube into two cubes or a biquadrate into two biquadrates and generally any power greater than two, into two powers with the same index. I have discovered truly amazing proof of this, but these margins are too narrow to put it here .

But then it turns out the recovered text is not at all the same that was published. Well, of course not that one! It's clear, if you publish the real text of the remarks made in the margins of the book, then no one will understand anything because that who writes them, does it not for someone, but only for himself. On the other hand, it is obvious that the content of the recordings in the margins is so that they could not be made in the course of reading the book and are the result of a very voluminous and many years of work that was done separately. It is obvious that in addition to these short notes there is yet a whole bunch of papers in draft and finishing versions with brief or detailed explanations. These papers have not always been prepared for printing and they still need to be brought to the desired state. Hence it is clear why the text was edited accordingly for publication in 1670. From the real notes all was removed that reveals the method of proof and the sequence of solving individual tasks, which have eventually led to the discovery of the FLT.

The restored remarks follow in chronological order and may diverge in time over years. The margins' records of the book were made after they were prepared separately, but it was not intended that they be published in the same view. On the contrary, in the final formulation of the FLT everything that could be concealed from the history and components of this brilliant scientific discovery, was completely removed. Only the final result has been remained, which turned out to be beyond the powers of all subsequent science right up to the beginning of the XXI century!

If this reconstruction of the original FLT recording on the margins of the book appeared 30 years earlier, it would have caused a quite stir in the scientific world since the sixth entry develops (!!!) this theorem to the general case with the different of power's indexes! However, this stir did nevertheless take place 25 years ago, and again it was caused not by a professional, but by an amateur interested in FLT with his conjecture corresponding to the restored sixth entry. Of course, to believe in all this is not easily, but also to invent such a thing is also hardly possible. Now we have to explain in more detail these restored entries in the margins and this will be done in the next points of our work and the same senator who started this whole story, will help us in this.

An unprecedented succession of failures, wrecks of secret hopes and defeats in the protracted for centuries storming of an impregnable fortress under name the Fermat's Last Theorem, turned into a such nightmare for science that even its very existence have been questioned. Like the fierce plague epidemic, the FLT not only deprived the minds of numerous amateur fermatists, scientists and unrecognized geniuses, but also very much contributed to the fact that the whole science was plunged into the abyss of uncontrollable chaos.

Pic. 12. Andrew Wiles

Already three and a half centuries have passed since the first publication of the FLT and twenty-five years after it was announced that in 1995 this problem was allegedly solved by Professor Princeton University USA Andrew Wiles. 6 6 It was a truly grandiose mystification, organized by Princeton University in 1995 after publishing in its own commercial edition "Annals of Mathematics" the “proof” of FLT by A. Wiles and the most powerful campaign in the media. It would seem that such a sensational scientific achievement should have been released in large numbers all over the world. But no! Understanding of this text is available only to specialists with appropriate training. Wow, now even that, which cannot be understood, may be considered as proof! However, for fairness it should be recognized that even such an overtly cynical mockery of science, presented as the greatest "scientific achievement" of the luminaries of Princeton University, cannot be even near to the brilliant swindle of their countrymen from the National Space Administration NASA, which resulted that the entire civilized world for half a century haven’t any doubt that the American astronauts actually traveled to the moon! However, once again it turned out this “epochal” event has nothing to do with the FLT! 7 7 The “proof”, which A. Wiles prepared for seven years of hard work and published on whole 130 (!!!) journal pages, exceeded all reasonable limits of scientific creativity and of course, him was awaiting inevitable bitter disappointment because such an impressive amount of casuistry understandable only to its author, neither in form nor in content is in any way suitable to present this as proof. But here the real wonder happened. Suddenly, the almighty unholy himself was appeared! Immediately there were influential people who picked up the "brilliant ideas" and launched a stormy PR campaign. And here is your world fame, please, many titles and awards! The doors to the most prestigious institutions are open! But such a wonder even for the enemy not to be wish because sooner or later the swindle will open anyway. “The proof” of Wiles rests solely on the idea proposed by the German mathematician Gerhard Frey. This idea was rated as brilliant, but apparently only because that it was an elementary and even very common error!!!

Pic. 13. Gerhard Frey

Instead of proving the impossibility of the Fermat equation a n+b n=c nin integers for n>2 here is proven only its incompatibility in the system with the equation y 2=x(x−a n)(x+b n). In a similar way any nonsense can be proven. If the same work would be presented by one of the students, any of the professors would quickly bring him to clean water pointing to the obvious substitution of the subject of proof. Nevertheless, this super sensational news with great fanfare was noted in the world's leading media. The most influential newspaper of the USA “The New York Times” has been reported this right on the front page … in whole 2 years before the appearance of the “proof” itself!!! Andrew Wiles as the author of the "proof" became a member of the French Academy of Sciences and the laureate of as many as 18 of the most prestigious awards!!! To cover this momentous event, the British broadcaster BBC released an enthusiastic film and also it was invited the writer Simon Singh who published a book in 1997 titled “The Fermat's Last Theorem. The story of a riddle that confounded the world's greatest minds for 358 years”.

Pic. 15. Simon Singh