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 ...

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 ...

Christopher Rasmussen does not work for, consult, own shares in or receive funding from any company or organization that would benefit from this article, and has disclosed no relevant affiliations ...

MATH30200 Number Theory, and MATH33300 Group Theory are recommended but not necessary. Integers and rational numbers are the first numbers we encounter, and as such they are, in a way the easiest ...