An equivalence relation on $\{-8,\dots,8\}$ is given by explicitly writing down the equivalence classes: \begin{align} [0]&=\{0\} \\ [1]&=\{1,-1\} \\ [2]&=\{2,-2,3,-3,5,-5,7,-7\} \\ [4]&=\{4,-4\} \\ [6]&=\{6,-6,8,-8\} \end{align} Is there a relation R on $\mathbb{Z}$ of the form $R=\{(a,b)\in \mathbb{Z}\times \mathbb{Z} | a,b \text{ satisfy } (*)\}$, which gives restricted to $\{-8,...,8\}\subset \mathbb{Z}$ exactly the above equivalence classes? Of course, I can define R by giving the elements explicitly. Im searching for a condition $(*)$ on the integers, which divides them in equivalence classes (compatible with the above ones).
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