This is my first post.
I'm having a bit of trouble getting started with some questions in a text I am going though. Most of the questions are similar,so if I can get through one of them, I'm assuming it would serve as a guide to getting through the rest. Here are a few of the presented questions:
- Let a ∈ Zn. Show that a and n are relatively prime if and only if there exists an element b ∈ Zn such that ab=1.
I realize that to show that numbers are relatively prime, I have to show that gcd(a,n)=1 -- I guess using Euclidean Algorithm, which I know how to do with actual numbers.
- Let a ∈ Zn. Show that a and n are relatively prime if and only if a's row in the multiplication table of Zn contains every element of Zn.
- Show that n is a prime number if and only if in the multiplication table for Zn, except for the first row, all elements of Zn appear in each row.
If someone can shed some light or provide some guidance, it is greatly appreciated!
I understand what the problem is asking, but I have no idea how to begin proving it.