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be nothing special if all these items did not contain … the most real and incredibly loud sensations! But to say only this about this book would be to say nothing about it. Alone only illustration of the real (!) text in the margins of a missing book (see Pic. 5) we have restored, can cause a real shock among experts of the main theme! They might think: "Is this really the same book with Pierre Fermat's notes in the margins?". But no, this book is not yet available. And since we still managed to find out, what was actually written in its margins where Fermat's Last Theorem should be located, we depicted this recording by all means available to us. If we compare this restored text with the one that was published back in 1670 (see Pic. 3), then it becomes obvious that these are completely different recordings!

      However, in our time, the Internet is also literally flooded with heart-rending screaming headlines about some sensations, which in fact are not, and their distributors resort to them only to raise the statistics of browsing. When it comes to science, if there are really sensations, then only in doses that cannot be captured by any statistics. The problem here is that the evaluations in the headlines are given by the distributors of information themselves who obviously should not be trusted. As for the content of this book, the situation here is principally different, since all the data here, assessments and conclusions can be checked by the most objective and incorruptible judge i.e. a regular calculator and anyone can always refer to it.

      In particular, if there is a suspicion that the restored Fermat’s record on the margins is nothing more than another fake among the sea of any other ones, they will prove to be not only nonconstructive, but also rejecting the opportunity itself to find out the real solution of the famous scientific problem. If this factor is not taken into account, then those who persist in such suspicions risk being in a very stupid position, since in this restored recording there is exactly what science still had no idea about. In fact, for science the FLT has always been just a puzzle, which for more than three centuries, could not be solved.

      Such a scornful attribution of one of the fundamental scientific problems to the sphere of intellectual entertainment led to the fact that real science began to give way to ideas that have nothing to do with it. As a result, it turned out that all reference books and encyclopedias in unison and categorically tell us that the FLT problem has long been solved, but in fact science has no idea about how things really are. If this were indeed the case, the consequences would be so significant that they would radically change the state of all science in general as a whole!!!

      Are you not believe? Well, judge for yourself, here is just one of these consequences. If the FLT is proven i.e. the solution in integers of the Fermat equation aⁿ+bⁿ=cⁿ for n>2 is impossible, this equation turns out to be the only (!!!) exception from the more general case A^x+B^y=C^z in which for any (!!!) given natural numbers x, y, z except of course x=y=z>2 may be calculate any number (!!!) of solutions in integers! And what now? Does science know, how to solve this general equation? Of course, no. Or perhaps science at least knows something about Fermat’s equations for children with magic numbers? Or about the wonderful Fermat’s binomial formula? Also no. However, the Soviet science fiction writer Alexander Kazantsev somehow incredibly way guessed about this formula, but mathematicians could not help him to derive it, so instead of a spectacular equation (see Pic. 1), he had to demonstrate an empty dummy.

      Apparently, he did not even suspect that he had to ask for help not from mathematicians, but from children, then the result of his fantastic guesstimate would have appeared much earlier than this book where this formula is derived exactly in the appropriate place i.e. in the restored FLT proof from the Fermat itself! If this proof (obtained 365 years ago!!!), will learned by children studying in ordinary secondary school, they can easily cope with solutions of equations containing the magic numbers. These numbers, unlike some that mathematicians work with, are real because they obey to the Basic theorem of arithmetic (BTA). But the trouble is that current science does not even suspect that this most fundamental of all theorems has not been proven up to now!!!

      But if science had become aware of this, then it would have no other choice as to accept BTA as an axiom since otherwise, science itself would simply disappear and then it could not be at all! Now, it will be a real surprise for science to find out that the problem of BTA proof was solved by the same Pierre Fermat and for this he used his own brand called the “descent method”. However, he could not divulge his proof since this would indicate an error of Euclid, in the proof of which he had it noticed, but this, not only at that time, as well as even now is inadmissible since gods by definition cannot be mistaken. It is also curious that without noticing the presence of BTA in the Euclid’s “Elements”, even such a giant of science as Karl Gauss exactly repeated the error of Euclid, what apparently also indicates his true divine origin.

      In this book the proof of BTA obtained by Fermat is now like the FLT restored and the loopholes for penetrating into science of all sorts of pseudo numbers are closed, although it will not be easily to cleanse them because the precedent for them was created by none other than the greatest scientist and mathematician Leonard Euler! Indirectly in this was also involved Karl Gauss proving the “basic theorem of algebra”, which without these allegedly numbers called “imaginary” or “complex” would be wrong. Long before Euler and Gauss such well-known scientists as Leibniz and Cardano expressed their categorical rejection to this kind of "numbers". But they did not know that these Kazantsev’s non-existent beings disobey to BTA since only in 1847 Ernst Kummer told this very unpleasant news for the first time to the entire scientific world. However, for some reason this scientific world up to now stubbornly unwilling to get rid of the illusion of what really doesn't exist at all! For example, the Euler’s formula that causes delight e^iπ+1=0 is in fact a complete nonsense that has nothing to do with science except perhaps to teach children not to believe in the reality of such tricks. Here even to them it is obvious that e^iπ = -1 and this is certainly an obvious bullshit since the imaginary number i = √-1 being here makes imaginary and meaningless everything in where it is presented.

      The main hero of our narration Pierre Fermat even in terrible dreams could not have imagined that only one of a whole hundred of his tasks [30] could even 325 years after the first publication of his works so much to discredit science, that it will turn out not only be incapacitated, but also literally standing in an head over heels position!!! Just in the period 1993-1995 it occurred immediately two events related to the FLT. The first is the Andrew Beal conjecture about the equation A^x+B^y=C^z, the proof of which allegedly allows to get FLT proof in one sentence. And the second is the Andrew Wiles’ FLT “proof” (which up to now nobody had understood), the news of which appeared in some incredible way in the newspaper "The New York Times" two years ahead of it! But then it was simply impossible to imagine what would happen when 25 years later it was suddenly found out that both of these events are pure misunderstandings!!!

      Beal conjecture to the difficulty of its proof is suitable perhaps for school-age children. But this is just incomprehensible to the mind how it could not be proven up to now even for a prize of a whole million dollars!!! Another no less surprising side of this conjecture is the lack of under-standing of how it is related to the proof of FLT, since what is written on this subject in Wikipedia is completely absurd. Nevertheless, Andrew Beal establishing such a large premium for his conjecture, clearly deserves universal respect, since with such a step he drew the attention of science on a theme, which had already taken place at Fermat in the above-mentioned restored FLT recording on Pic. 5.

      The announced competition to prove the Beal conjecture does not allow us to clarify the solution of this problem in this book, because it can cause a real stir in the scientific world. Despite the simplicity of the proof of this conjecture, its consequences will be a loud sensation, since they will allow us really to get the simplest proof of the FLT. On the other hand, this will be too modest a result for the Beal conjecture, because its scientific potential is incomparably more powerful and impressive. To fix this situation to the best, this book will offer a more meaningful formulation of this problem, which called here the Beal Theorem, that not only confirms the correctness of conjecture, but also opens up the possibility of solving the equation A^x+B^y=C^z for any natural powers except the case x=y=z>2.

      As for the Wiles’ FLT “proof”, it rests only on the Gerhard Frey’s idea, where again (for

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