List questions from totient-function

Published on 03 Dec 2013 - 9:53

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Prove that $n$ divides $\phi(a^n -1)$ where $a, n$ are positive integer without using concepts of abstract algebra

Published on 05 Dec 2013 - 16:23

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RSA and phi function

Published on 06 Dec 2013 - 7:58

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For every positive integer n greater than $2$, $\phi(n)$ is an even integer.

Published on 27 Mar 2026 - 23:57

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I suppose $(a,m)=(a-1,m)=1$, show that $1+a+a^2+\ldots+a^{\phi(m)-1}\equiv0\pmod m$

Published on 06 Dec 2013 - 19:36

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How to show that $2730\mid n^{13}-n\;\;\forall n\in\mathbb{N}$

Published on 06 Dec 2013 - 21:09

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Let $a,m\in\mathbb{N^*}$, with $m>1$, such that $(a,m)=1$. Show that, if $n_1\equiv n_2\pmod{\phi(m)}$, then $a^{n_1}\equiv a^{n_2}\pmod m$

Published on 06 Dec 2013 - 21:28

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Counting Chains of Bounded Types

Published on 28 Mar 2026 - 21:06

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Suppose that n > 1. Prove that n divides $ φ (2^n - 1) $ .

Published on 16 Dec 2013 - 7:18

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Euler's phi function and perfect numbers

Published on 27 Mar 2026 - 2:01

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Proof that the euler totient function is multiplicative, correctness?

Published on 25 Mar 2026 - 23:15

139

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Prove that $\varphi(n) = n \cdot \prod\limits_{i=1}^l \frac{p_i - 1}{p_i}$

Published on 04 Jan 2014 - 18:31

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Define ≡ in this situation?

Published on 04 Jan 2014 - 21:04

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Properties of the euler totient function

Published on 07 Jan 2014 - 8:08

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Why is Euler's totient function equal to $(p-1)(q-1)$ when $N=pq$ and $p$ and $q$ are prime in a clean intuitive way?

Published on 07 Jan 2014 - 8:29

List Question

Prove RSA formula to be correct

Prove that $n$ divides $\phi(a^n -1)$ where $a, n$ are positive integer without using concepts of abstract algebra

RSA and phi function

For every positive integer n greater than $2$, $\phi(n)$ is an even integer.

I suppose $(a,m)=(a-1,m)=1$, show that $1+a+a^2+\ldots+a^{\phi(m)-1}\equiv0\pmod m$

How to show that $2730\mid n^{13}-n\;\;\forall n\in\mathbb{N}$

Let $a,m\in\mathbb{N^*}$, with $m>1$, such that $(a,m)=1$. Show that, if $n_1\equiv n_2\pmod{\phi(m)}$, then $a^{n_1}\equiv a^{n_2}\pmod m$

Counting Chains of Bounded Types

Suppose that n > 1. Prove that n divides $ φ (2^n - 1) $ .

Euler's phi function and perfect numbers

Proof that the euler totient function is multiplicative, correctness?

Prove that $\varphi(n) = n \cdot \prod\limits_{i=1}^l \frac{p_i - 1}{p_i}$

Define ≡ in this situation?

Properties of the euler totient function

Why is Euler's totient function equal to $(p-1)(q-1)$ when $N=pq$ and $p$ and $q$ are prime in a clean intuitive way?

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