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**Kitizhi** Define the equivalence relation S by S = {(x,y)ͼAxA | 5 divides (x^2-y^2)}.

Determine the partition of A that is induced by S.

I am not exactly sure how to do this one but from what I gather from my textbook it seems to sorta start like this..

Given

$\displaystyle

S \cdot S = \{(x,y) \in AxA | 5 divides (x^2-y^2)\}

$

$\displaystyle

=\{(x,y) \in A^2 | (x^2-y^2) = 5k, \forall k \in Z\}

$

$\displaystyle

=\{(x,y) \in A^2 | (x^2 = 5k+y^2, \forall k \in Z\}

$

$\displaystyle

=\{(x,y) \in A^2 | y^2 = x^2-5k, \forall k \in Z\}

$

Am I doing this correctly? On the right track?