1.

On Z, define R as follows: a,b in Z, aRb if 3|(a^(2) - b^(2)), then R is an equivalence relation on Z. Equivalence class containing 1, that is, [1] is given by

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{...,-3,0,3,6,...]
{...,-3,-1,1,3,...]
{...,-4,-2,1,2,4,5,7,8,...}
{...,-4,-2,-1, 1,2,4,5,7,8, ...}

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