Number Theory Meets Computability Theory

Asking Questions about Equations In this article, we consider the problem of solving certain types of equations (called polynomial equations). For example, imagine you are given the equation4-x2= 0 and asked to do the following: determine if there exists a solution for the variable x in integers. Since it is easy to come up with a single solution in this case, namely x= 2, we can use this specific solution to answer this question in the affirmative. In contrast, it should be clear that a slightly modified equation such as 2-x2= 0 does not have a solution, which can easily be checked by hand.