Polynomial Diophantine Equations

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.

• 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).