Mathematical puzzles that originally arose from the practical context of selling fruits have evolved into complex algebraic challenges known as Fruit Diophantine equations. Delving into the intricacies of these foundational problems, researchers from the Department of Mathematics at SRM University-AP Prof. Kalyan Chakraborty (Senior Professor), and Dr Kalyan Banerjee (Assistant Professor),  along with Ms Ankita Das, PhD Scholar, have published a new study titled “Generalized Fruit Diophantine Equation And Super Elliptic Curves.” Featured in Monatshefte Fur Mathematik, a Q2 journal with an impact factor of 0.8, the study explores the properties of these unique mathematical structures. While the classic Fruit Diophantine equation () is already known to have no integer solutions, the research team successfully generalized this equation and proved that, under specific conditions, these broader equations also lack integer solutions. By investigating the rational points on certain superelliptic curves, this collaborative research advances fundamental number theory and deepens our understanding of these fascinating mathematical phenomena.

Practical implications: This equation that we considered sheds some light on the geometry of the Jacobian of certain high genus curves and we can talk about its rational points, which is difficult to find out.

Read the full paper here