Aspire Faculty ID #19281 · Topic: UGC NET Computer Science June 2019 (Paper II) · Just now
UGC NET Computer Science June 2019 (Paper II)

Consider the Euler's phi function given by

$\phi(n)=n\prod\left(1-\dfrac{1}{p}\right)$

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

Solution

We have,

$45=3^2\times 5$

So, prime divisors of $45$ are $3$ and $5$.

Using Euler's phi function,

$\phi(45)=45\left(1-\dfrac{1}{3}\right)\left(1-\dfrac{1}{5}\right)$

$=45\times \dfrac{2}{3}\times \dfrac{4}{5}$

$=24$

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