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Web-Technologies
October 7, 2023
TIFR PHD CS & SS 2018
October 7, 2023
Web-Technologies
October 7, 2023
TIFR PHD CS & SS 2018
October 7, 2023

UGC NET June-2019 CS Paper-2

Question 23
Consider Euler’s Φ function given by
Φ(n)=nπp|n(1-(1/p))
Where p runs over all the primes dividing n. What is the value of Φ(45)?
A
3
B
12
C
6
D
24
Question 23 Explanation: 
Φ(45) → Φ(9*5)
→ Φ(32 * 5)
→ Φ(32) * Φ(5)
→ Φ(32 – 3,(2-1)) * (5-1)
= 24
Remember Formula:
If p is prime then Φ(p) = (p-1)
and if p is not prime and it’s in prime power k from then Φ(pk) = pk – p(k-1)
Correct Answer: D
Question 23 Explanation: 
Φ(45) → Φ(9*5)
→ Φ(32 * 5)
→ Φ(32) * Φ(5)
→ Φ(32 – 3,(2-1)) * (5-1)
= 24
Remember Formula:
If p is prime then Φ(p) = (p-1)
and if p is not prime and it’s in prime power k from then Φ(pk) = pk – p(k-1)

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