Algebra Solutions: Addition of residue classes of integers is associative

Prove that addition of residue classes in $\mathbb{Z}/(n)$ is associative. (You may assume that it is well defined.)

We have

$(\overline{a} + \overline{b}) + \overline{c}$	=	$\overline{a+b} + \overline{c}$
	=	$\overline{(a+b)+c}$
	=	$\overline{a+(b+c)}$
	=	$\overline{a} + \overline{b+c}$
	=	$\overline{a} + (\overline{b} + \overline{c})$ ,

since integer addition is associative. $\blacksquare$

Algebra Solutions