For ordinary integers, the following is true. If ab D 0, then a D 0 or b D 0. The

Chapter 37, Problem 37.10

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For ordinary integers, the following is true. If ab D 0, then a D 0 or b D 0. The analogous statement for Zn is not necessarily true. For example, in Z10, 2 5 D 0 but 2 6D 0 and 5 6D 0. However, for some values of n (e.g., n D 5) it is true that a b D 0 implies a D 0 or b D 0. For which values of n 2 does the implication a b D 0 () a D 0 or b D 0 hold in Zn? Prove your answer

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