8.1. Understanding the functionality of groups, cyclic groups and subgroups is important for the use of public-key cryptosystems based on the discrete logarithm problem. That’s why we are going to practice some arithmetic in such structures in this set of problems. Let’s start with an easy one. Determine the order of all elements of the multiplicative groups of: 1. Z∗ 5 2. Z∗ 7 3. Z∗ 13

its 60

4 x 12 = 48

3 x 4 = 12

48 + 12 = 60

yeeeet

the number of possible outcomes that do not show a 1 on the first spinner and show the number 4 on the second spinner is 2.

spinner 1 spinner 2

1                     1

1                     2

1                     3

1                     4

2                   1

2                   2

2                   3

2                   4   = not 1, and 4

3                   1

3                   2

3                   3

3                   4 = not 1, and 4

only 2 outcomes have passed the given condition.

step-by-step explanation:

for the free

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