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Recent questions tagged euler-phi-function
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UGC NET CSE | June 2019 | Part 2 | Question: 63
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 $\phi(45)$? $3$ $12$ $6$ $24$
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 t...
Arjun
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Arjun
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Jul 2, 2019
Combinatory
ugcnetcse-june2019-paper2
euler-phi-function
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2
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UGC NET CSE | June 2019 | Part 2 | Question: 70
Consider the following statements: $S_1$: For any integer $n>1, \: a^{\phi(n)} \equiv 1(mod \: n)$ for all $a \in Z_n^*$ , where $\phi(n)$ is Euler’s phi function. $S_2$: If $p$ is prime, then $a^p \equiv 1(mod \: p)$ for all $a \in Z_p^*$. Which one of the following is/are correct? Only $S_1$ Only $S_2$ Both $S_1$ and $S_2$ Neither $S_1$ nor $S_2$
Consider the following statements:$S_1$: For any integer $n>1, \: a^{\phi(n)} \equiv 1(mod \: n)$ for all $a \in Z_n^*$ , where $\phi(n)$ is Euler’s phi function.$S_2$:...
Arjun
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Arjun
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Jul 2, 2019
Set Theory & Algebra
ugcnetcse-june2019-paper2
euler-phi-function
set-theory&algebra
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