ABOUT ONE BINARY PROBLEM IN A CLASS OF ALGEBRAIC EQUATIONS AND HER COMMUNICATION WITH THE GREAT HYPOTHESIS OF FERMAT

In this  article  the author  introduces  the notion  of the binary mathematical statement A n 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 B n:  ”whether has the equation for a preset value n some decision x n”  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.