Theorems on infinite sequences with definite qualities

L.E.Abramov

Saint-Petersburg, Russia

ale@mail.spbnit.ru

The theorem (Theorem 1) is proven, which states conditions, when no elements pair with 2 given qualities exists for any finite number of infinite sequences first elements with definite qualities. Generalizations of Theorem 1 (Theorem 2 and 3, and Theorem 3 Consequence) are shown.

Theorem 1 may be applied to solve some problems of Theory of Numbers, and, in future, it may become the base for new research trend in this field of mathematics. In particular, it is shown that Theorem 1 permits to prove easily Fermats Great Theorem (problem only recently solved by E.Wiles, using Taniyama-Shimura hypothesis proof).

The work essence extends beyond pure mathematics, based on concepts included into Statistical Physics by L.Boltzmann. At the same time we tried in detail, on generally accepted level of mathematical requirements, to demonstrate concepts used in this work.

Theory of Probability and Entropy method are used in Theorem 1 demonstration. (Entropy method is ''Boltsman cells in the phase space'' method in Statistical Physics generalization).

For the first time the strict mathematical grounds of Entropy method are given (using the proof of Statement 2).

The problems considered in this work were not raised earlier, as well as the approach applied to solve these problems was not formerly in proper mathematics.

 

The extract from the reference to the Editorial Board from V.F.Zaitsev, Guest Editor, Professor of the Department of Mathematical Analysis at A.I. Gertsen’s RGPU, Doctor of Physics and Mathematics, who represented the article by L.E. Abramov:

 

Invitation to discussion

 

We strongly recommend you to read the article, where on the basis of entropy method and probability approach the author states and proves some theoretical-numeric principles, the application of which exceeds the boundaries of the set topic and can be spread to the number of vital questions of mathematical simulating (modeling). The principles are supported by the original approach worked out by the author and mainly based on the probability theory and statistics principles.

I haven’t found any mistakes in the statements. It would be possible to emphasize some “inaccuracy” in definitions, which to some extent dim the sense of objects in question. But the fact that the suggested approach is based on the principles of statistical physics, which are not definitely mathematical. Not being the expert in the probability theory, the author of the article can not completely quarantee the correctness of his work. In particular, the identification of zero probability and non-realization of the event at the point of proceeding to endless limit gives rise to several doubts even at the presence of evidences, featuring no evident “flops”. The results, announced in this work, are of a priority and completely unique character.