Abstract
The large number of problems in the theory of the numbers possessing one characteristic sign called by us binary mathematical statements from the natural parameter which in the time of Pythagoras and Euclid still aren’t solved was prompted to us that the reason of such situation should be looked for in the mathematics bases. We have entered concept of the binary mathematical statement depending from natural parameter and have specified axiomatic of natural numbers of Peano, having added one axiom called by us the axiom of descent which is interpretation of a so-called method of descent of Fermat by means of which he has proved the Great Hypothesis for a special case of n=4. By means of a descent axiom we managed to receive a large number of the results published in Russian. Wishing to expand a readership, we have decided to give the review of our results which are already published in Russian without proofs and to add new results among which the algorithm of search of large prime numbers is dominating with proofs.
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