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An application of Lagrange's Theorem. Let n E N. Let E, be the subset of Z,, defined by {[21]: i Z}. For instance, E6

An application of Lagrange's Theorem. Let n E N. Let E, be the subset of Z,, defined by {[21]: i Z}. For instance, E6 = {[0], [2], [4]}, and E ={[0], [2], [4]}. Prove that E, is a subgroup of Zn if and only if n is even.

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