BMath Bachelor of Mathematics Number Theory and Discrete Mathematics

Question 1

Which of the following best describes a prime number?

Accepted Answer

A number greater than 1 with no positive divisors other than 1 and itself

Answer

A number divisible by 2

Answer

An even number greater than 2

Answer

A number that is the square of an integer

Question 2

The greatest common divisor gcd(48, 36) equals:

Accepted Answer

12

Answer

6

Answer

18

Answer

9

Question 3

Fermat's Little Theorem states that if p is prime and gcd(a, p) = 1, then:

Accepted Answer

a^(p−1) ≡ 1 (mod p)

Answer

a^p ≡ a (mod p)

Answer

a² ≡ 1 (mod p)

Answer

p ≡ 1 (mod a)

Question 4

How many integers from 1 to 10 are coprime to 10?

Accepted Answer

4

Answer

2

Answer

5

Answer

6

Question 5

The Fundamental Theorem of Arithmetic states that every integer n > 1:

Accepted Answer

Has a unique prime factorization

Answer

Can be written as a sum of two primes

Answer

Is either prime or a perfect square

Answer

Has at most two prime factors

Question 6

In modular arithmetic, 17 mod 5 equals:

Accepted Answer

2

Answer

1

Answer

3

Answer

4