List questions from totient-function

Published on 29 Sep 2019 - 16:27

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Proof that if $\gcd(a,n) = 1$ then $a^k \equiv a^{k \bmod \phi(n)} \pmod {\!n}$

Published on 30 Sep 2019 - 19:44

156

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Observations needed to justify an algebraic passage in proof of a property of $\varphi$ (Totient function)

Published on 15 Mar 2014 - 18:01

508

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On proving $n = \sum_{d\mid n}\varphi(d)$

Published on 16 Mar 2014 - 0:26

2.3k

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Summation involving totient function: $\sum_{d\mid n} \varphi(d)=n$

Published on 17 Mar 2014 - 7:59

6.3k

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Find all n such that $\phi(n) = n/2$

Published on 18 Mar 2014 - 14:08

1k

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Prove that if $d \mid n \in \mathbb{N}$, then $\varphi(d) \mid \varphi(n)$.

Published on 25 Mar 2026 - 7:43

79

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I want to prove that if $n$ is composite and $\varphi(n) \mid (n - 1)$, then $n$ is squarefree

Published on 20 Mar 2014 - 11:04

2.9k

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Is there a recursive formula for Euler's Totient function

Published on 25 Mar 2026 - 7:40

2.9k

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When does $ ϕ(3n)=3ϕ(n) $?

Published on 25 Mar 2014 - 21:11

647

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Derivation of the lower bound of Euler's Phi Function

Published on 30 Mar 2014 - 22:29

79

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How to show that if $\phi(n)$ equals to n itself, then n must be 1?

Published on 31 Mar 2014 - 12:38

216

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What is known about the solutions to $\varphi(a)+\varphi(b)=\varphi(a+b)$?

Published on 02 Apr 2014 - 15:09

17.3k

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Euler totient function sum of divisors. Theorem 2.2 Apostol

Published on 03 Apr 2014 - 0:17

158

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Sum of Euler Phi equalities

Published on 05 Apr 2014 - 23:13

List Question

Sum of prime numbers related to Euler's totient function

Proof that if $\gcd(a,n) = 1$ then $a^k \equiv a^{k \bmod \phi(n)} \pmod {\!n}$

Observations needed to justify an algebraic passage in proof of a property of $\varphi$ (Totient function)

On proving $n = \sum_{d\mid n}\varphi(d)$

Summation involving totient function: $\sum_{d\mid n} \varphi(d)=n$

Find all n such that $\phi(n) = n/2$

Prove that if $d \mid n \in \mathbb{N}$, then $\varphi(d) \mid \varphi(n)$.

I want to prove that if $n$ is composite and $\varphi(n) \mid (n - 1)$, then $n$ is squarefree

Is there a recursive formula for Euler's Totient function

When does $ ϕ(3n)=3ϕ(n) $?

Derivation of the lower bound of Euler's Phi Function

How to show that if $\phi(n)$ equals to n itself, then n must be 1?

What is known about the solutions to $\varphi(a)+\varphi(b)=\varphi(a+b)$?

Euler totient function sum of divisors. Theorem 2.2 Apostol

Sum of Euler Phi equalities

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