WorksheetsExistence of Primitive Roots
Total questions: 11
Worksheet time: 5mins
Name
Class
Date
1.
1.Which of the following has a primitive root?
a)
5
b)
15
c)
16
2.
What is the primitive root of 1?
a)
1
b)
2
c)
none
3.
φ(3)=?
a)
2
b)
3
c)
4
d)
5
4.
φ(18)=?
a)
6
b)
3
c)
15
d)
17
5.
Which theorem states that " If m is not 𝑝^𝑎 or 〖2𝑝〗^𝑎 then m does not have a primitive root?
a)
Theorem 62
b)
Theorem 63
c)
Theorem 64
d)
Theorem 65
6.
φ(17)=?
a)
14
b)
15
c)
16
d)
17
7.
How many primitive roots does 7 have?
a)
2
b)
3
c)
4
d)
5
8.
Given φ(10) = 4, what are its possible order?
a)
1,2,4
b)
1,2,4,5
c)
1,2,4,5,8
d)
1,2,4,5,10
9.
What are the possible primitive roots of modulo 9?
a)
1,2,4
b)
1,2,4,5
c)
1,2,4,5,7
d)
1,2,4,5,7,8
10.
φ( φ(14))=?
a)
2
b)
6
c)
7
d)
13
11.
What are the possible order of element in modulo 9?
a)
1,2
b)
1,2,3
c)
1,2,3,6
d)
1,2,3,6,9
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