Diophantine equations stand at the interface of algebra, geometry and arithmetic, seeking integer or rational solutions to polynomial equations. Classical problems such as Pythagorean triples and ...

Back in the year 2000, the Clay Mathematics Institute announced the “Millennium Prize problems”, which is basically a group of the most important maths problems that still remain unsolved. The ...

Several years ago one of us, Toni, asked another of us, Marco, to come to his office at the Institute of Photonic Sciences, a large research center in Castelldefels near Barcelona. “There is a problem ...

Diophantine equations, classical problems in number theory, seek integer or rational solutions to polynomial relations. When approached through algebraic number theory, these equations are studied ...