Diophantine equations are a type of mathematical equation that seeks integer solutions. Named after the ancient Greek mathematician Diophantus, these equations typically take the form of a polynomial equation where the variables are required to be whole numbers. An example is the equation x^2 + y^2 = z^2, which looks for integer values of x, y, and z. These equations can be simple or complex, depending on the number of variables and the degree of the polynomial. Solving Diophantine equations often involves techniques from number theory, and some famous problems, like Fermat's Last Theorem, are special cases of these equations.