Number Theory - I

What does Euler’s Totient Function, ϕ(n), calculate?

• The number of prime factors of n

• The number of positive integers less than n that are relatively prime to n

• The sum of all prime numbers less than n

• The number of ways to factor n

If p is a prime number, what is ϕ(p)?

• p - 1

• p + 1

• p/2

• p^2 - 1

What is ϕ(10)?

• 2

• 3

• 4

• 5

What is ϕ(15)?

• 6

• 8

• 10

• 12

What is ϕ(8)?

• 3

• 4

• 6

• 7

Phi(41) =

• 5

• 7

• 40

• 42

Phi(440) =

• 160

• 170

• 180

• 190

Phi(210) =

• 42

• 44

• 46

• 48

If n is a prime number squared, say p² , then φ(p²) = ?

• p−1

• p

• p² − p

• p² − 1

φ(100) = ?

• 40

• 60

• 50

• 80