The original version of this story appeared in Quanta Magazine. The world of mathematics is full of unreachable corners, where unsolvable problems live. Now, yet another has been exposed. In 1900, the ...

It’s a puzzle that’s baffled experts since the 1950s, but now a solution for the Diophantine equation has finally been cracked. The problem asks if all whole numbers could be expressed as the sum of ...

Research in group theory has long embraced equations as a means to elucidate the structure and behaviour of groups. In particular, Diophantine problems—those surrounding the existence and ...

Hot on the heels of the ground-breaking 'Sum-Of-Three-Cubes' solution for the number 33, a team led by the University of Bristol and Massachusetts Institute of Technology (MIT) has solved the final ...

This is a preview. Log in through your library . Abstract In this paper, we consider subbalancing numbers formed by using the third balancing number in the Diophantine equation. We obtain some ...

A polynomial parametrization for the group of integer two-by-two matrices with determinant one is given, solving an old open problem of Skolem and Beurkers. It follows that, for many Diophantine ...

Your mathematics teacher at school will have told you that you can only solve a set of simultaneous equations if there are as many equations as there are variables, but that is because they don’t ...