TY - BOOK ID - 8284687 TI - An Introduction to Diophantine Equations : A Problem-Based Approach AU - Andreescu, Titu. AU - Andrica, Dorin. AU - Cucurezeanu, Ion. PY - 2010 SN - 0817645489 9786613568977 0817645497 1280391057 PB - Boston, MA : Birkhäuser Boston : Imprint: Birkhäuser, DB - UniCat KW - Diophantine analysis. KW - Diophantine equations. KW - Electronic books. -- local. KW - Diophantine equations KW - Mathematics KW - Physical Sciences & Mathematics KW - Algebra KW - Indeterminate analysis KW - Diophantic equations KW - Equations, Diophantic KW - Equations, Diophantine KW - Equations, Indefinite KW - Equations, Indeterminate KW - Indefinite equations KW - Indeterminate equations KW - Mathematics. KW - Algebra. KW - Number theory. KW - Number Theory. KW - Number theory KW - Forms, Quadratic KW - Diophantine analysis KW - Mathematical analysis KW - Number study KW - Numbers, Theory of UR - https://www.unicat.be/uniCat?func=search&query=sysid:8284687 AB - This problem-solving book is an introduction to the study of Diophantine equations, a class of equations in which only integer solutions are allowed. The material is organized in two parts: Part I introduces the reader to elementary methods necessary in solving Diophantine equations, such as the decomposition method, inequalities, the parametric method, modular arithmetic, mathematical induction, Fermat's method of infinite descent, and the method of quadratic fields; Part II contains complete solutions to all exercises in Part I. The presentation features some classical Diophantine equations, including linear, Pythagorean, and some higher degree equations, as well as exponential Diophantine equations. Many of the selected exercises and problems are original or are presented with original solutions. An Introduction to Diophantine Equations: A Problem-Based 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. The work uniquely presents unconventional and non-routine examples, ideas, and techniques. ER -