
ILO 6 - Arithmetic Function
Quiz
•
Mathematics
•
Professional Development
•
Practice Problem
•
Medium
Lonwell Pagkaliwagan
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12 questions
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1.
MULTIPLE CHOICE QUESTION
20 sec • 1 pt
Which function counts the number of positive divisors of a positive integer n?
σ(n)
ϕ(n)
d(n)
μ(n)
2.
MULTIPLE CHOICE QUESTION
20 sec • 1 pt
Which statement is TRUE?
𝜙 is additive
𝜙(n) > n
𝜙 is multiplicative for any integers
𝜙 is multiplicative only for relatively prime numbers
3.
MULTIPLE CHOICE QUESTION
20 sec • 1 pt
Which of the following is TRUE about a multiplicative function?
f(1) = 0 for all multiplicative function
f(ab) = f(a) + f(b) when gcd(a,b) = 1
f(ab) = f(a) f(b) when gcd(a,b) = 1
f(ab) = f(a) f(b) for all integers a and b Answer: C
4.
MULTIPLE CHOICE QUESTION
20 sec • 1 pt
What is the value of σ(7)?
7
8
14
15
5.
MULTIPLE CHOICE QUESTION
20 sec • 1 pt
What is the value of ϕ(15)?
6
8
10
12
6.
MULTIPLE CHOICE QUESTION
20 sec • 1 pt
What is the value of 𝜙(7), if 7 is a prime number?
5
6
7
8
7.
MULTIPLE CHOICE QUESTION
20 sec • 1 pt
Given f(15)=f(5)f(3), and 5 and 3 are coprime, this expression shows that:
f(n) is not defined
f(n) is completely multiplicative
f(n) is additive
f(n) is multiplicative
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