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 ...

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 ...

The Monthly publishes articles, as well as notes and other features, about mathematics and the profession. Its readers span a broad spectrum of mathematical interests, and include professional ...

An American mathematician has cracked part of a problem that had remained unsolved for 64 years. Andrew Booker, Reader of Pure Mathematics at the University of Bristol in the U.K., worked out how to ...