The brute force approach for solving diophantine equation is a well. Humans have understood how to compute the area of a circle for a long time. A problembased approach is intended for undergraduates, advanced high school students and teachers, mathematical contest participants including olympiad and putnam competitors as well as readers interested in essential mathematics. Math circles lesson 1 introduction to linear diophantine. Introduction to diophantine equations in the early 20th century, thue made an important breakthrough in the study of diophantine equations. The work uniquely presents unconventional and nonroutine. There are many, many forms of diophantine equations, but equations of the sort that. Titu andreescu, dorin andrica an introduction to diophantine equations. If n 2, there are no nontrivial1 solutions in integers to the equation. A diophantine equation is an algebraic equation for which rational or integral solutions are sought.
A diophantine problem over q is concerned with the solutions either in q or in z of a. Use the euclidean algorithm to compute the following gcds. Math circles solution set 1 introduction to linear. An introduction to diophantine equations springerlink. It focuses on diophantine equations and the qualitative description of their solutions rather than. Probably the most famous diophantine equation is the one representing fermats last theorem. An introduction to number theory and diophantine equations. You may have just thought without hesitation why, the area of a circle of radius r is. By nding all integral points on certain elliptic and hyperelliptic curves.