 However, whether quantification over rationals can also be substituted for quantification over the integers is a notoriously hard open problem.The MRDP theorem states that a set of integers is Diophantine if and only if it is computably enumerable.A set of integers "S" is computably enumerable if and only if there is an algorithm that, when given an integer, halts if that integer is a member of "S" and runs forever otherwise.