Welcome guest
You're not logged in.
255 users online, thereof 0 logged in


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

| | | | created: 2014-02-20 21:37:44 | modified: 2019-03-09 17:21:54 | by: bookofproofs

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 (Euclid)

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

Edit or AddNotationAxiomatic Method

This work was contributed under CC BY-SA 3.0 by:

This work is a derivative of:


Bibliography (further reading)