Axis Journal of Mathematical Statistics and Modelling
Structures Of Pythagorean Triples And Fermatâs Last Theorem
Abstract
Jacqueline Wotzel
Pythagorean triples are groups of three natural numbers and are a simplification of the notation. They satisfy the Pythagorean theorem when each number is squared and the sum of the first two numbers equals the square of the third number. For example, the triple (3, 4, 5) represents 32 + 42 = 52 . Fermat`s last theorem states that there are no natural numbers for x, y, z, n in this general form xn +yn = zn , where is n greater than 2.
The following article shows all the arithmetic relationships that can be found in the Pythagorean triples. Structures in these triples and calculation methods are presented. It also explains how to classify them and how to create infinitely many new Pythagorean triples in these classes. To obtain new classes of Pythagorean triples, is to create with one number the first triple of a new class and continue infinitely in this class by knowing the universal arithmetic structures and relations.