Suppose that n1, n2, . . . , nk are positive even

Chapter 8, Problem 51E

(choose chapter or problem)

Suppose that \(n_1, n_2, \ldots , n_k\) are positive even integers. How many elements of order 2 does \(Z_{n_1} \oplus Z_{n_2} \oplus \ldots \oplus Z_{n_k}\) have? How many are there if we drop the requirement that \(n_1, n_2, \ldots , n_k\) must be even?

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