an equation of the form is a formula

an indeterminate equation in which both the solution and the terms must be whole numbers (after Diophantus of Alexandria, c

a polynomial equation with integral coefficients to which only integral solutions are sought

An equation which is required to be solved by integers.Thus the diophantine equation 2 2 - 3 2 = 5 has the integer solution

In mathematics, a Diophantine equation is an indeterminate polynomial equation that allows the variables to be integers only. Diophantine problems have fewer equations than unknown variables and involve finding integers that work correctly for all equations. In more technical language, they define an algebraic curve, algebraic surface or more general object, and ask about the lattice points on it.