Problem 4. Consider ϕ : (Z100, +100) → (Z100, +100) defined by ϕ([x]100) = [41x +...

Problem 4. Consider ϕ : (Z100, +100) → (Z100, +100) defined by ϕ([x]100) = [41x + 19]100. a.) Show that ϕ is well-defined. b.) Use the fact that 61 · 41 = 2501 to argue that the function ϕ is one-to-one. c.) Is ϕ onto? Why or why not. Suppose that y is in the image of ϕ, find an element x so that ϕ(x) = y. [The answer will be dependent on the value of y.] Then prove that the found element works. d.) Is ϕ a homomorphism?

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Expert Solution

Colby Messinger answered 2 years ago

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