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October 7, 2023TIFR PHD CS & SS 2018
October 7, 2023UGC NET June-2019 CS Paper-2
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Question 23
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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)?
Φ(n)=nπp|n(1-(1/p))
Where p runs over all the primes dividing n. What is the value of Φ(45)?
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3
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12
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6
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24
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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)
→ 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)
→ 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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