Hilbert's 10 Problem

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 $$\begin{array}{c}4-x^2=0\end{array}$$ 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.