Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 1.1 Exercise 1.1.3
Prove that addition of residue classes in $\mathbb{Z}/(n)$ is associative. (You may assume that it is well defined.)
Solution: We have \begin{align*} (\overline{a} + \overline{b}) + \overline{c} = &\ \overline{a+b} + \overline{c}\\ = &\ \overline{(a+b)+c}\\ = &\ \overline{a+(b+c)}\\ = &\ \overline{a} + \overline{b+c}\\ = &\ \overline{a} + (\overline{b} + \overline{c}), \end{align*} since integer addition is associative.
