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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
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