An Introduction to Diophantine Equations: A Problem-Based ApproachThis problem-solving book is an introduction to the study of Diophantine equations, a class of equations in which only integer solutions are allowed. 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. |
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An Introduction to Diophantine Equations: A Problem-Based Approach Titu Andreescu,Dorin Andrica,Ion Cucurezeanu No preview available - 2010 |
An Introduction to Diophantine Equations: A Problem-Based Approach Titu Andreescu,Dorin Andrica,Ion Cucurezeanu No preview available - 2011 |
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assume called clear Clearly congruent consider contradiction cube defined denote Determine Diophantine Equations distinct divides divisible elements equal equation becomes equation is equivalent equation x2 Example exist fact Fermat’s Find Find all pairs follows fundamental solution gcd(a given gives hence identity implies impossible induction inequality infinitely infinitely many solutions integers n integers the equation integral solutions least loss Mathematical Olympiad method minimal multiple nonnegative integers nonzero integers Note obtain pairs parity Pell's Pell’s equation perfect square positive integers possible prime divisor Proof Prove Pythagorean quadratic residue reduces relation relatively prime Remark result ring Romanian satisfying satisfying the equation sequence solutions in positive solvable solvable in positive Solve Suppose Theorem tion Titu Andreescu triples triples x,y,z true unique unit values Write the equation written yields