Suppose that G is an Abelian group of order 35 and every element of G satisfies...

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Suppose that G is an Abelian group of order 35 and every element of G satisfies the equation x35 = e. Prove that G is cyclic. Does your argument work if 35 is replaced with 33? Suppose that G is an Abelian group of order 35 and every element of G satisfies the equation x35 = e. Prove that G is cyclic. Does your argument work if 35 is replaced with 33?