Homework #2: Due: September 11, 2020
Points: 20
Question 1 [10 points]. Modular Arithmetic: Compute the following without a calculator:
i. 243 * 154 mod 10 (Hint: a*b mod c = ((a mod c) * (b mod c)) mod c)
ii. 8 * (3/17) mod 10 (Hint: In mod system, a, a+10, a+20, a+30, a+40, etc. are all equal)
iii. 8$^{12}$ * 7$^{14}$ mod 10
iv. 8$^{12}$ * 7$^{14}$ mod 17
Question 2 [10 points].
i. Show the elements of groups $Z_{14}$ and $Z^*_{14}$
ii. Find the order of 9 in $Z_{14}$
iii. Find (if it exists) the multiplicative inverse of 5 $\in$ $Z_{14}$ (integer ring)
iv. Is $Z^*_{14} = \{1, 3, 5, 9, 11, 13\}$ a cyclic group? If so, what is its order and the generator element?
What to submit? Submit a pdf file with your answers via the Blackboard. Show your work