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

A series of unsolved puzzles in number theory called Diophantine problems date back to 3,700 years ago. Over the years mathematicians have whittled away at them, and recent work has made significant ...

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 famously difficult mathematical problem resisted solution for over 40 years. Mathematicians have finally resolved it by following an intuition that links number theory to physics. Mathematical ...

Hot on the heels of the ground-breaking 'Sum-Of-Three-Cubes' solution for the number 33, mathematicians have solved the final piece of the famous 65-year-old math puzzle with an answer for the most ...

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 ...

Every December 8 for years, Julia Robinson blew out the candles on her birthday cake and made the same wish: that someday she would know the answer to Hilbert’s 10th problem. Though she worked on the ...

Diophantus of Alexandria revolutionized algebra with Arithmetica, pioneering symbolic notation and abstract number theory.