AMC12 Number Theory 3

Question 1

What is Euler's totient function phi(12)?

Accepted Answer

4

Answer

6

Answer

3

Answer

8

Question 2

How many solutions does x^2 = 1 (mod 8) have among {0,1,2,...,7}?

Accepted Answer

4

Answer

2

Answer

1

Answer

0

Question 3

What is the largest prime factor of 2310?

Accepted Answer

11

Answer

7

Answer

13

Answer

5

Question 4

How many trailing zeros does 50! end with?

Accepted Answer

12

Answer

10

Answer

8

Answer

15

Question 5

If n=2^3*3*5^2, how many ordered pairs (a,b) satisfy lcm(a,b)=n?

Accepted Answer

105

Answer

75

Answer

36

Answer

45

Question 6

What is the remainder when 2^200 is divided by 3?

Accepted Answer

1

Answer

2

Answer

0

Answer

4