Diophantine equations, named after the ancient mathematician Diophantus of Alexandria, are polynomial equations whose solutions are sought in integers or rational numbers. From the simplest linear and ...

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 ...

For decades, a math puzzle has stumped the smartest mathematicians in the world. x 3 +y 3 +z 3 =k, with k being all the numbers from one to 100, is a Diophantine equation that's sometimes known as ...

A set of puzzles called Diophantine problems are often simple to state but hard to solve—though progress could have big implications for the future of mathematics Diophantine geometry is the field of ...

In mathematics, no researcher works in true isolation. Even those who work alone use the theorems and methods of their colleagues and predecessors to develop new ideas. But when a known technique is ...

A number theorist with programming prowess has found a solution to 33 = x³ + y³ + z³, a much-studied equation that went unsolved for 64 years. Now, Andrew Booker, a mathematician at the University of ...

An eminent mathematician reveals that his advances in the study of millennia-old mathematical questions owe to concepts derived from physics. Mathematics is full of weird number systems that most ...