Such an unusual character of our perceptions concerning to science, can cause a very negative reaction. But here we can confess that we had very good reasons for this because we managed to look in those very “heretical recordings” of Fermat. For greater persuasiveness we directly here will show one of the examples of our capabilities and accurately reproduce the real text of the most intriguing recording of the Fermat's Last theorem in the margins of Diophantus' "Arithmetic", which instance did belong to the author and disappeared unknown whither. So, in this place (see Pic. 5), we gain sight of several notes to the task under the number VIII made in Latin at different times. In translation they look like this:

1st entry: However, it is impossible to decompose C into two other C or QQ into two other QQ. Both proof by the descent method.

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.