Titlebook: Quadratic Diophantine Equations; Titu Andreescu,Dorin Andrica Textbook 2015 Springer Science+Business Media New York 2015 Pell‘s equation.

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1389-2177 esented will shed light on important open problems.Includes .This monograph treats the classical theory of quadratic Diophantine equations and guides the reader through the last two decades of computational techniques and progress in the area. These new techniques combined with the latest increases

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Textbook 2015hniques and progress in the area. These new techniques combined with the latest increases in computational power shed new light on important open problems. The authors motivate the study of quadratic Diophantine equations with excellent examples, open problems and applications. Moreover, the exposit

champaign

Why Quadratic Diophantine Equations?,In order to motivate the study of quadratic type equations, in this chapter we present several problems from various mathematical disciplines leading to such equations. The diversity of the arguments to follow underlines the importance of this subject.

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Debark

,General Pell’s Equation,This chapter gives the general theory and useful algorithms to find positive integer solutions (.,?.) to general Pell’s equation (4.1.1), where . is a nonsquare positive integer, and . a nonzero integer.

Cardioversion

,Equations Reducible to Pell’s Type Equations,An interesting problem concerning the Pell’s equation . is to study when the second component of a solution (.,?.) is a perfect square.

thrombus

Diophantine Representations of Some Sequences,In 1900, David Hilbert asked for an algorithm to decide whether a given Diophantine equation is solvable or not and put this problem tenth in his famous list of 23.

REIGN

Other Applications,In [122] and [123] it is proven that there are infinitely many positive integers . such that 2. + 1 and 3. + 1 are both perfect squares. The proof relies on the theory of general Pell’s equations.