Diophantine Equation

Abstract

In the first chapter we have given some definations, theorems, lemmas on Elementary Number Theory. This brief discussion is useful for next discussion on the main topic.
We know that there are two type of Diophantine equation i.e., (i) Linear Diophantine equation, (ii) Non-linear Diophantine equation. In the second chapter we have discussed about the solutions of both kind of Diophantine
equation. Here we have given the necessary and sucient condition for existence the solution of a Linear Diophantine equation and also discussed about the Non-linear Diophantine equation and discussed Fermat's Last theorem. Pell's equation is a special type of Diophantine equation. The history of Pell's equation is very interesting. In the last section we have given some methods to find the fundamental solution of the Pell's equation.