Chapter 2 definitions

Question 1

Define the well ordering axiom

Answer 1

Every non-emtpty set of positive integers has a smallest number

Question 2

Define the division algorithm

Answer 2

Let n and d >=1 be integers. There exists uniquely determined inters q and r such that n = qd +r and 0<=r<d. q and r are called quotient and remainder respectively

Question 2

Define a divisor

Answer 2

if n and d are integers, d is called a divisor of n if n = qd for some integer q. we write d|n.

Question 3

Define relatively prime integers

Answer 3

Two integers m and n are called relatively prime if gcd(m,n) = 1

Question 4

Define the greatest common divisor

Answer 4

If m and n are integers, not both zero, an integer d is called the greatest common divisor of m and n, written gcd(m,n) if

(i) d>=1
(ii) d|m and d|n
(iii) if k|m annd k|n, then k|d