Geometric Note to the Last Fermat’s Theorem

: In this paper, we concerned with geometrical interpretation of tangent line to the curve and grid points which can be used to some illustration of Fermat's last theorem. With tangent line we find segment at axis x, y. With using this segments we make a ratio to find condition to grid point at the curve from equation of Last Fermat’s theorem.


Introduction
French lawyer Pier Fermat is one of the world's most renowned mathematicians. He dealt with mathematics in his free time and was very successful in this field. His ''little,, theorem is well known in the theory of numbers.
For any integer number a and p is primary number, the number − is an integer multiple of The proof is possible to find in [1]. So called Fermat's last theorem was not proved in the field of maths for a long time. It was proved in 1994 by a British mathematician Andrew Wiles in his work called Modular elliptic curves and Last Fermat's theorem, which had more than a 100 pages [4]. Fermat's last theorem can be proved as follows: No three positive integers x, y, and z can satisfy the equation for any integer value of n greater than two.
In this paper, we look at the geometric interpretation of Fermat's last theorem.
Firstly, we use the curves which are represented with equations from Fermat's theorem.
Secondly, we use the tangent line. We need ordinates of tangent point, because numbers of ordinates are numbers of solution Fermat's equation for Real number.

The Meaning of The Last Fermat's Theorem
The base of modern proof was on the Taniyama-Shimura-Weil's conjecture. This conjecture connecting topology and number theory. It is focused to connect between elliptic curve and modular forms. That is means that every elliptic curve at form = + + + defined over the rational numbers is a modular form in disguise. This conjecture is important to elliptic curves that are used on the cryptography. At 1982 Gerhard Frey made elliptic curve at form = − + which is connected with the Last Fermat Theorem at form + = where l is primes. At 1985 Jaean -Pierre Serre shown that Frey curve could not be modular. And definite connect between Taniyama-Shimura-Weil's conjecture and the Last Fermat Theorem made Ken Ribet at 1990 with epsilon conjecture. And finally after 358 years of history was definite proof by Andrew Wiles. How we can see, this proof made new mathematic method and connect and connect different parts of mathematics.

Diophantine Equations
Diophantic equations are indefinite polynomial equations, whose solutions are only integers numbers. History about Diophantine equation began about 3. century with work Hellenistic mathematics Diophantus from Alexandria with Aritmetica. His work was inspirited by special problems from real life. Now the Diophantine problems are difficult part of number theory and it is a reason for their interest history.

Geometric Number Theory
The Diophantine equations are difficult problem and this is a reason why mathematicians use geometry method to solve a problems task. The most works about geometry number theory made Herman Minkowski. He studied n-dimensional space with integer vector. This space is symmetry to rotations and translations.

Using Geometry to Last Fermat Theorem
In E2 is function represented the last Fermat theorem is curve , = . We can use a tangent line in the point N) & , & *. Now we can write a equation for tangent line: We use substitution From the lasts conditions (11) and (13) and (14) we can see only one possibility for ^, _ ∈ M and %, , , & , & ∈ ] is only for = 2 and _ = 1.