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

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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