Properties of Integers

Course: CSCI 1900

Divisibility

• An integer divides if there exists an integer such that
• → “a divides b”
  • → is divisible by
  • → is not divisible by

Properties of Division

• Distributive Property → if and , then
• Common Factor → if , then for all integers
• Associative Property → if and , then

Remainder Theorem

• ,
• Where is the dividend, is the divisor, is the quotient, and is the remainder
• →

Floor

• Round down to the nearest integer

Integer Division + Modulus

• Integer Division → only returns the quotient
  • Also known as “floor division”
• Modulus → returns only the remainder

Congruence + Modular Arithmetic

• If , then
  • because