Integers

Question 1

What are the 2 ways to use he Well-Ordering Principle (W.O.P.)?

Answer 1

1) to show a subset has a least element

2) as a base of a contradiction

Question 2

What does the q and r in this equation represent b=qa + r ?

Answer 2

q - quotient

r - remainder

Question 3

What is the definition of a prime?

Answer 3

P is a prime if and only if the only positive divisors of P are 1 and P

Question 4

What is the definition of composite?

Answer 4

a number is composite if and only if there is a number other than 1 and itself that is a divisor of the number

Question 5

What is the definition of a common divisor?

Answer 5

a common divisor of a and b, is an integer g such that g/a and g/b. The greatest common divisor, denoted by gcd(a,b), of a and b is the largest positive common divisor of a and b

Question 6

What is the gcd(0,0)?

Answer 6

0

Question 7

Is the gcd(a,b) equal to the gcd(-a,b)?

Answer 7

Yes

Question 8

What is Bezout’s Theorem?

Answer 8

there exists integers m and n such that gcd(a,b) = ma + nb

Question 9

What is the definition of coprime?

Answer 9

two integers a and b are coprime if and only if gcd(a,b)=1

Question 10

What is the Fundamental Theorem of Arithmetic

Answer 10

n is an integer greater than 1. Then there exists a unique finite collection of primes {p1, p2,…,pr} and a unique sequce of strictly positive integers a1, a2,…,ar such that 2