Recap

Question 1

Equivalence relation

Answer 1

Let R be a relation on a set. We say that A is an equivalence relation if it satisfies the following properties. A is reflexive
A is symmetric
A is transitive

Question 2

Congruent modulo n

Answer 2

Let nEN, and a,bEZ. a is congruent to b mod n if n | a-b.

Question 3

Congruence class

Answer 3

the set of integers (x) that are congruent to a mod n

Question 4

The set of congruence classes modulo n

Answer 4

Let n e N. We define the set of congruence classes modulo n to be Zn = { [a]n : a e z}

Question 5

Ring of integers modulo n

Answer 5

The set Zn with addition and multiplication defined as follows 
Let x, y e Zn and chose x0, y0 e Z s.t 
x = [x0]n and y=[y0]n
- x + y = [x0 + y0]n
- xy = [x0y0]n