+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 the umpteenth time in the past 350 years!) an elementary error was made!!! In this case, if something has been proven it is the complete inability of science to notice such errors, which must be teaching by schoolchildren. As a result, these events took place in such a way that on the FLT problem and its generalization in the form of the Beal conjecture, science once again became a victim of misunderstandings i.e. the current situation with the solution of the FLT problem is no better than the one that was 170 years ago, when the German mathematician Ernst Kummer provided proof of the FLT particular cases for prime numbers from the first hundred of the natural numbers.

With a such amount of knowledge available to current science, its helpless state seems as something irrational and even unthinkable. Nevertheless, it permeates whole of it through and far from only the FLT problem, but also in general wherever you poke, the same thing happens everywhere – science shows its inconsistency so often and in so many questions that they simply cannot be counted. The only difference is that some of them still find their solution, but with the FLT science has been stuck for centuries. However, the greatness of this problem lies in the fact that it, apart from purely methodological difficulties, points to some aspects of a fundamental nature, which have such a powerful potential that, if it succeeds in uncovering of it, science will be able to make an unprecedented breakthrough in its development.