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## Main Question or Discussion Point

Suppose that ##n,j \in \mathbb{N}##, ##j \in [0, n-1]##, and ##n~|~2j##. Why is it the case that ##j = 0## or ##2j = n##? This is used in a proof of something else, but I am getting tripped up on this part. I know it has to do with the fact that ##j \in [0, n-1]##. Is it because ##n## can't ever divide 2 or j separately and the quantity 2j is never greater than or equal to 2n, then if it divides anything it must divide 0 or ##n##?