Congruence and Arithmetic.

Suppose \(a \equiv b \pmod{n}\) and \(c \equiv d \pmod{n}\text{.}\) Then the following hold:

1. \(a+c \equiv b+d \pmod{n}\text{.}\)

2. \(a-c \equiv b-d \pmod{n}\text{.}\)

3. \(ac \equiv bd \pmod{n}\text{.}\)