Please consider the following question:
Determine the order of all the elements of the following multiplicative groups. You can write a C or Java program to do this.
Now note that $21$ is not a prime number and since the question refers to a multiplicative group, I would expect that means the operator for the group is multiplication mod 21. This means that the number $7$ should have an inverse. That is, there should be a number x, such that $(7x)\,mod\,\,21\,\,=\,1$. I claim that no such $x$ exists. What am I missing?