Modular Arithmetic - BSIS 1A

a system of arithmetic for integers, which considers the Remainder

• Modular Arithmetic

• Division

• Divisibility Theorems

• Division Algorithm

(51+29) mod 3

• 3 (modulo 4)

• 2 (modulo 3)

• 3 (modulo 2)

• 4 (modulo 3)

(99+1) mod 7

• 7 (modulo 2)

• 0

• 0 (modulo 7)

• 2 (modulo 7)

(325+69) mod 13

• 3 (modulo 13)

• 4 (modulo 13)

• 5 (modulo 13)

• 6 (modulo 13)

(95-58) mod 8

• 3 (modulo 8)

• 4 (modulo 8)

• 5 (modulo 8)

• 0

(63-27) mod 6

• 1 (modulo 6)

• 2 (modulo 6)

• 3 (modulo 6)

• 0

(258-89) mod 14

• 0

• 1 (modulo 14)

• 2 (modulo 14)

• 0 (modulo 14)

(39x19) mod 9

• 2 (modulo 9)

• 3 (modulo 9)

• 4 (modulo 9)

• 0

(29x51) mod 4

• 0

• 3 (modulo 4)

• 4 (modulo 4)

• 5 (modulo 4)

(123x55) mod 14

• 1 (modulo 14)

• 2 (modulo 14)

• 3 (modulo 14)

• 0