 Diophantine equations

Diophantine equations are a class of polynomial equations for which we seek integer solutions. Named after the ancient Greek mathematician Diophantus, these equations are typically of the form: \[ P(x_1, x_2, ..., x_n) = 0 \] where \( P \) is a polynomial with integer coefficients, and \( x_1, x_2, ..., x_n \) are unknown variables that we want to solve for in the integers.