Chapter: Divisibility

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

  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

Chapters: 1
Examples: 2
Explanations: 3

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