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  3. 3 in this question quotinvertiblequot means invertible with respect to...

Question: 3 in this question quotinvertiblequot means invertible with respect to...

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3. In this question, invertible means invertible with respect to the multiplication of Zn (a) [1 points] Determine all of the invertible elements of Z. (b) [3 points| Let p be a prime number. Determine the number of the invertible elements of Zpa. You should justify your answer. (c) [3 points] Let p be an odd prime number. Show that for every k E N, the only elements x E Zpk such that x2-1 in Zpk are x-1 and x-pf-1. (d) [1 point] Show that part (c) does not hold when p - 2.

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