The relation ~ on $\mathbb{Z}$ defined by $x$ ~ $y$ iff ${x}^2$ = ${y}^2$. Explicity find the equivalence classes [0],[4],[-72].
Can someone please help me understand how to find equivalence classes. I have not clue how to do this problem.
Thank you.
If $c \in \mathbb Z$, then $[c]$ is the set of all integers $d$ such that $c^2=d^2$. For $c=4$, the equality becomes $d^2= 4^2 = 16$. What integers $d$ satisfy this equality? How about the other values of $c$?