Some Notes on Pythagorean Triples in Diophantine Equations

Abstract

There exist solutions of algebraic equation in the study of the early mature conclusion. Within the scope of the complex numbers sets, the 5 times following algebraic equation has formula solution. However, when we put the solution of the limit in the range of natural numbers or within the scope of rational number, the equation becomes Diophantine equation. These solutions are not easily found. In this paper, all kinds of solution of the Pythagorean equation were studied. The derivation of using chord method got a formula of rational number solution. This formula can be used to easily get countless set of integer solutions.