A Diophantine equation is a type of polynomial equation that seeks integer solutions. Named after the ancient Greek mathematician Diophantus, these equations often take the form of ax + by = c , where a , b , and c are integers, and x and y are the unknowns that must also be integers. These equations can vary in complexity, from simple linear forms to more complicated higher-degree equations. Solving Diophantine equations is a significant area of study in number theory, as it involves finding whole number solutions and understanding the properties of integers.