Modular arithmetic

• \(x \equiv y (\text{mod} : n) \leftrightarrow (x-y) : \text {mod} : n = 0\)

Addition Tables

• Z mod 4

  +	0	1	2	3
  0	\((0 + 0) \mod 4 = 0\)	1	2	3
  1	\((1 + 0) \mod 4 = 1\)	2	3	0
  2	\((2 + 0) \mod 4 = 1\)	3	0	1
  3	\((3 + 0) \mod 4 = 3\)	0	1	2

Multiplication tables

• Z mod 4

  x	0	1	2	3
  0	\((0 \cdot 0) \mod 4 = 0\)	0	0	0
  1	\((1 \cdot 0) \mod 4 = 0\)	1	2	3
  2	\((2 \cdot 0) \mod 4 = 0\)	2	0	2
  3	\((3 \cdot 0) \mod 4 = 0\)	3	2	1