3. (a) Let n ∈ N with n ≥ 2 and consider (Zn, ⊕). If a...

3. (a) Let n ∈ N with n ≥ 2 and consider (Zn, ⊕). If a ∈ Zn, show that a = a −1 if and only if n | 2a. What conditions on n would guarantee that no element is equal to its own inverse?

(b) Let p be prime and consider (Up, ). Under what conditions does a ∈ Up satisfy a = a −1 ? Can you specifically identify the elements that satisfy this condition?

Expert Solution

Colby Messinger answered 6 months ago

For each positive integer, n, let P({n}) =(1/2^n) . Consider the events A = {n :...

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