List questions from totient-function

Published on 25 May 2015 - 17:39

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For $n > 2, n \in \mathbb{Z}$, show the sum of integers coprime to $n$ in the range $[1,n-1]$ is equal to $\frac{1}{2}n \phi(n)$

Published on 30 May 2015 - 17:36

788

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Find $7^{999,999}$ modulo (10)

Published on 11 Jun 2015 - 7:54

74

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Show that $(M^{e})^d \equiv M$ (mod n).

Published on 11 Jun 2015 - 8:31

147

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Show that $10^{n(p-1)}\equiv 1\pmod{\! 9p}$ for $p\ge 7$

Published on 13 Jun 2015 - 14:56

173

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prove that for each $n \in\mathbb N$ odd, $\phi(n) \ne 2^{32}$

Published on 13 Jun 2015 - 16:44

317

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Find remainder using euler function?

Published on 13 Jun 2015 - 20:56

29

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Show that $\sum_{d \mid p-1} T(d) = p-1$ where $p$ is prime and $T(d) = \# \{a \mid 1 \le a \le p - 1, \, (a,\,p-1)=d \}$.

Published on 14 Jun 2015 - 0:36

1.9k

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Is there $\phi(n)=n/6$

Published on 17 Jun 2015 - 14:01

111

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Determining whether there exists an $a$ such that $\text{ord}_{17}(a) = 4$.

Published on 17 Jun 2015 - 19:31

110

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Determining whether there exists an integer $a$ such that $\text{ord}_{20}(a) = 8$.

Published on 18 Jun 2015 - 2:49

1.2k

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Understanding Primitive roots

Published on 18 Jun 2015 - 5:40

366

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Proof to a property of Euler's totient function

Published on 25 Mar 2026 - 19:59

167

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Sum of super exponentiation

Published on 02 Jul 2015 - 6:30

4.2k

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The equation $\phi (x)=n$ has only a finite number of solutions.

Published on 03 Jul 2015 - 18:17

List Question

Proving that $\varphi(n)=n\prod (1-1/p)$ without using multiplicativity

For $n > 2, n \in \mathbb{Z}$, show the sum of integers coprime to $n$ in the range $[1,n-1]$ is equal to $\frac{1}{2}n \phi(n)$

Find $7^{999,999}$ modulo (10)

Show that $(M^{e})^d \equiv M$ (mod n).

Show that $10^{n(p-1)}\equiv 1\pmod{\! 9p}$ for $p\ge 7$

prove that for each $n \in\mathbb N$ odd, $\phi(n) \ne 2^{32}$

Find remainder using euler function?

Show that $\sum_{d \mid p-1} T(d) = p-1$ where $p$ is prime and $T(d) = \# \{a \mid 1 \le a \le p - 1, \, (a,\,p-1)=d \}$.

Is there $\phi(n)=n/6$

Determining whether there exists an $a$ such that $\text{ord}_{17}(a) = 4$.

Determining whether there exists an integer $a$ such that $\text{ord}_{20}(a) = 8$.

Understanding Primitive roots

Proof to a property of Euler's totient function

Sum of super exponentiation

The equation $\phi (x)=n$ has only a finite number of solutions.

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