UGC NET CSE | June 2019 | Part 2 | Question: 63

Question

Consider the Euler’s phi function given by

$$\phi(n) = n \underset{p/n}{\Pi } \bigg( 1 – \frac{1}{p} \bigg)$$

where $p$ runs over all the primes dividing $n$. What is the value of $\phi(45)$?

• A. $3$
• B. $12$
• C. $6$
• D. $24$

Answer 1

Right answer $4.  24$

Euler’s Totient function =

Where $p = $all prime factors of $n$

Now given $n=45$

Then prime factors of $45= 3,5$

$\phi \left ( 45 \right )=45\times \left ( 1-\frac{1}{3} \right )\times \left ( 1-\frac{1}{5} \right )=24$

https://www.google.com/amp/s/www.geeksforgeeks.org/eulers-totient-function/amp/

Comments

The question is from which section?