Polynomial Diophantine Equations

A Systematic Approach

AvBogdan Grechuk

Inbunden, Engelska, 2024

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Häftad

534 kr

Beskrivning

This book proposes a novel approach to the study of Diophantine equations: define an appropriate version of the equation’s size, order all polynomial Diophantine equations by size, and then solve the equations in order. Natural questions about the solution set of Diophantine equations are studied in this book using this approach.

Produktinformation

Utgivningsdatum:2024-09-02
Mått:155 x 235 x 50 mm
Vikt:1 384 g
Format:Inbunden
Språk:Engelska
Antal sidor:807
Förlag:Springer International Publishing AG
ISBN:9783031629488

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Mer om författaren

Bogdan Grechuk is an associate professor at the University of Leicester, UK. As a child, he took part in various mathematics competitions, including the International Mathematical Olympiad, where he won gold and silver medals. His research includes many areas of pure and applied mathematics. He is also interested in the exposition of mathematics to undergraduate and high school students.

Innehållsförteckning

1 Explicit Solutions to Small Equations.- 2 Existence of Polynomial Parametrizations.- 3 Equations in Two Variables.- 4 Explicit Descriptions of the Solution Sets.- 5 The Finiteness Problem.- 6 Existence of Non-Trivial Solutions to Homogeneous Equations.- 7 Existence of Integer Solutions.- 8 Alternative Orderings of Diophantine Equations.- 9 Solutions to Selected Exercises (by Ashleigh Wilcox).