The Arithmetic in Galois’s Equations

In this article I demonstrate the method for solve Galois’s equations, is applying simply arithmetic in his coefficients.


Introduction
Throughout the latter century Galois's polynomials have taken great relevancy in mathematics and by it, the great number of articles that to they reference. By associating Galois theory with the problems of the Diophantine equations (elliptical curves) and in the inverse problem (Hilbert). Nevertheless none of them reflected an process of beginning to the solution, and if has got improved with the Newton's-Rapson Algorithm. Therefore the article that I present will be of interest and relevancy for the mathematicians.
Therefore if we apply arithmetic we have Is to say: ax n + bx (n−1) + cx (n−2) + · · · + · · · < jx 2 with which x Is equality generalized for all the Galois's equations. [6], [7], [10] In the " (1.2 )", we have the same thing is to say that: We differentiate the values of the coefficients in two form: random coefficient and determinant coefficients. (the determinant coefficients are designated for the existence of Galois's equations,; his numerical value is major that of the random. Therefore to solve Galois's equations we woll do the following: we take two of the coefficients of major value; example (e, d), factoring both values in such a way that, the common value of them is the value that corresponds to him to (x) it is to say.
(e ∩ d) = (a n ; b; b × a) = x Now well, if the equation belong to the group of Galois's " (1.3 )" we will have the numbers (m.x). And therefore we divide all this coefficients by (m), for his checking.
If the presented equations allows to deduce the value give (x) we apply the process and, we substitute (x) for his value, if we verify that is correct, we will have an equation falsified.

Discussion
Galois's inverse problem. [5], [9] Any finite group that converge on (0), admits multiply all his coefficients for a number (m), and to have a polynomial of the same degree that that of the finite group.
; this is reflected in the example 6.
We observe also that the inverse problem, allows to give the solution of the polynomial, because.
P (x) = ax n + bx n−1 + cx n−2 With (n = 7) and the finite group is an elliptical curve such as ex n−4 + f x n−5 + gx n−6 + h; with (e = 1) [ see 12], [4] if we substitute in the polynomial, the elliptical curve we have that.
P (x) = ax n + bx n−1 + cx n−2 + dx n−3 + y 2 = 0 Wihebery the polynomial is solved because we know value of the variable with equation Enfer [12]. The same we will have if in the polynomial, there are one quadratic function.

Conclusion
The value of the variable in Galois's polynomials the we know, with the factoring of two of the coefficients of major value of such form that. e ∩ d = (a n ; b; b × a) = x The developed process in this paper contradict Abel theorem because we resolve Galois's equation at apply laws of of arithmtic over the coefficints.