If we could somehow look into this cache, what will we see there? To begin with, let's try to find some simple tasks there. For example, the one that Fermat could offer today for secondary school students:

Divide the number x^>n−1 by the number x−1, or the number x^>2n−1 by

the number x±1, or the number x^>2n+1+1 by the number x+1.

It is obvious that students with the knowledge of solving such a task will be simply a head over the current students who are trained in the methods of determining the divisibility by only some small numbers. But if they else know a couple of the Fermat's theorems, they can easily solve also the more difficult problem:

Find two pairs of squares, each of which adds up to the same number

in the seventh power, for example,

221^>7=151114054^>2+53969305^>2=82736654 ^>2+137487415^>2

Compared to the previous task where calculations are not needed at all, in solving this task, even with a computer calculator you have to tinker with half an hour to achieve a result, while apart from understanding the essence of the problem solution, you need to show a fair amount of patience, perseverance and attention. And who understands the essence of the solution, will be able to find other solutions to this problem.30

Of course, such tasks can cause a real shock to today's students and especially to their parents who will even demand not to “dry the brains” of children. But if children's brains are not filled with elementary knowledge and not trained by solving the corresponding tasks, they will wither by themselves. This is proven by the statistics of the steady decline in today's students IQ compared with their predecessors. Really in fact, the above tasks are only a warm-up for the young generation, but children could produce a real furor for mathematicians offering them some simple Fermat's theorems about magic numbers (see Pt. 4.4.). And this is else a big question, could these theorems being solved by today's professors or will they again need some three hundred years and the story with the FLT will repeat? However, the chances of them in contrast to previous times, are very high because magic numbers are a direct consequence of the same “truly amazing” proof of the FLT, about the existence of which we have direct written evidence from Fermat himself.

Reconstruction of this proof was briefly published as early as 2008 [30], but the unholy was on the alert and presented this event so, that modern science disoriented by the false notion that the problem was solved long ago, has not paid on this any attention. However, all secret sooner or later becomes clear and the decisive word in spite of everything, still remains for science. The question now is only when this science will finally awaken and comes to his senses. The longer it will be in a blissful state of oblivion, the sooner the terrible events will come that already now beginning to shake our world like never before.

In order for science to win a well-deserved victory over the gloom of ignorance and mass disinformation, which are triumphant today, it needs very little. For the beginning it is necessary simply to search for the very cache, in which such secrets of science are hidden, that have not lost their relevance for three and a half centuries.31 Even if the papers found in the cache will be unreadable, the very fact of the existence of the cache will be evidence that science is moving in the right direction and the results will not be long in coming.

We already did something in this direction when we restored the FLT recording in the margins of Diophantus 'Arithmetic' (see pic. 5 and the translation in the end of Pt. 1). Now, by all means, we need to get a complete picture of the whole sequence of events that led to the discovery of the FLT in its final wording published in 1670. It will not be easily at all, but since we got involved in this story, now we have nowhere to retreat and we will strain all our forces to achieve the aim. Fortunately, for this we have all the opportunities granted to us from above to get the coveted access to the cache of the Toulousean senator.