Free Printable Number theory

1.

The remainder when 82 ! is divided by 83

a)

-1

b)

1

c)

0

2.

Fermat's number is of the form

a)

$F_n=2^{2^n}+1$

b)

$F_n=2^n+1$

c)

$F_n=2^2+n$

3.

(a)

4.

(a)

5.

(a)

6.

(a)

7.

(a)

8.

$Ifn=2^k\ \ \ then\ \ \ \ \phi\left(n\right)\ \ \ is$

a)

n

b)

n/2

c)

n/3

9.

$\phi\left(5!\right)=$

a)

32

b)

36

c)

42

10.

How many positive factors of 23

a)

2

b)

3

c)

4

11.

$If\ n\ can\ be\ written\ as\ product\ of\ k\ distinct\ primes\ then\ \ \tau\left(n\right)=$

a)

$2^k$

b)

2

c)

k

12.

$The\ \ value\ of\ \ ϕ(18)\ \ \ is$

a)

6

b)

4

c)

10

13.

$\phi\left(p^e\right)=$

a)

$p^e\left(1-\frac{1}{p}\right)$

b)

$p^e\left(1+\frac{1}{p}\right)$

c)

$p\left(1-\frac{1}{p}\right)$

14.

$If\ \ \ p\ \ \ is\ \ \ a\ \ \ prime\ \ then\ \ \phi\left(p\right)=$

a)

p-1

b)

p

c)

p+1

15.

$The\ \ value\ \ of\ \ \ τ(6120)\ \ \ is$

a)

48

b)

36

c)

28

Number theory

Total questions: 15

Worksheet time: 13mins

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