Number Theory Meets Computability Theory

Solving Equations In this article1, we consider the problem of solving certain types of equations (called polynomial equations). For example, imagine you are given the equation $$ \begin{align} 4 - x^{2} = 0 \end{align} $$ 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.