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
Create a list with two columns for every group, where each row contains an element a and the order ord(a). (Hint: In order to get familiar with cyclic groups and their properties, it is a good idea to compute all orders "by hand", i.e., use only a pocket calculator. If you want to refresh your mental arithmetic skills, try not to use a calculator whenever possible, in particular for the first two groups