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 polynomial equations 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 can lead to interesting results, such as the famous Fermat's Last Theorem, which states that no three positive integers can satisfy the equation x^n + y^n = z^n for n > 2.