About one binary problem in a class of algebraic equations and her communication with the great hypothesis of fermat

Author: 
Kochkarev B.S

In this article the author introduces the notion of the binary mathematical statement An from natural parameter n and refined axiomatic Peano natural numbers by adding the axiom of descent which is algebraic interpretation of the so-called method of descent Fermat. The known class of the Diophantine equations Fermat is reduced to some class of the algebraic equations from natural parameter n, n ≥ 3 (degree of polynomial). It is proved that concerning binary statement Bn: ”whether has the equation for a preset value n some decision xn” the corresponding classes of the algebraic and Diophantine equations are equivalent. We show that the constructed class of the algebraic equations has rational decision only for n = 4. For n = 3, 4 the constructed class of the algebraic equations has decisions in radicals, and for n ≥ 5 this classes of the equations isn’t solvable at all. Thus also it is prove, that the Great Hypothesis of Fermat is correct with the small precision: the class Diophantine equations of Fermat have not the decision non-only in integers but and in the rational field.

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