The title is exercise 2.2 in The Fundamental Theorem of Algebra.
The hint for the problem is: Find the value of $\frac{1}{3}$ in $\mathbb{Z}_{13}$
(please realize that my knowledge of the subject is what I read in Chapter 2)
I have gotten that $x = -\frac{1}{3}$.
I know that $\mathbb{Z}_{13}$ is the integers modulo 13. Thus $x \equiv n \pmod{13}$? for some integer n, $0\le n < 13$.
Thus for $x – n = km$ for some integer $k$, with $m \neq 0$ and an integer.
How does m divide $(x-n)$, when $(x-n)$ is not an integer, if $x = -\frac{1}{3}$????