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Chapter: Divisibility

Divisibility is one of the most important properties of integers which is fundamental to number theory. We start with some basic definitions.

Table of Contents

1. Definition: Divisor, Complementary Divisor, Multiple
2. Proposition: Sign of Divisors of Integers
3. Proposition: Finite Number of Divisors
4. Definition: Divisor-Closed Sets
5. Proposition: Divisibility Laws
6. Definition: Sets of Integers Co-Prime To a Given Integer
7. Definition: Even and Odd Numbers
8. Lemma: Division with Quotient and Remainder
9. Proposition: Least Common Multiple
10. Proposition: Greatest Common Divisor
11. Proposition: Relationship Between the Greatest Common Divisor and the Least Common Multiple
12. Definition: Co-prime Numbers
13. Proposition: Greatest Common Divisor of More Than Two Numbers
14. Proposition: Least Common Multiple of More Than Two Numbers

Mentioned in:

Chapters: 1
Examples: 2
Explanations: 3

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