Question

What is the probability for which :$\gcd ((\phi(n),n-1)=1 ) $ for integers?

score 233 · Answer 1 · 2026-04-29 12:46:11

233

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What is the probability for which :$\gcd ((\phi(n),n-1)=1 ) $ for integers?

Published on 29 Apr 2026 - 12:46

score 59 · Answer 2 · 2026-05-07 11:17:36

59

Views

On variations of Erdős squarefree conjecture: presentation and a question as a simple case

Published on 07 May 2026 - 11:17

score 3k · Answer 3 · 2026-05-07 14:19:48

3k

Views

Let $\phi$ be Euler's totient function. Prove that $\phi(3n) = 3\phi(n)$ iff 3 divides n.

Published on 07 May 2026 - 14:19

score 242 · Answer 4 · 2026-05-10 16:29:41

242

Views

What is the explicit formula for $\Phi(x)=\sum\limits_{n=1}^x\phi(n)$?

Published on 10 May 2026 - 16:29

score 1000 · Answer 5 · 2026-05-07 11:30:19

1000

Views

Euler totient function equation: $\varphi(n)=42$

Published on 07 May 2026 - 11:30

score 587 · Answer 6 · 2026-04-14 17:07:19

587

Views

Show there are infinitely many positive integers $k$ such that $\phi(n)=k$ has exactly two solutions where $n$ is a positive integer

Published on 14 Apr 2026 - 17:07

score 342 · Answer 7 · 2026-05-10 13:27:18

342

Views

Questions on Convergence of Explicit Formulas for $f(x)=\sum\limits_{n=1}^x a(n)$ where $a(n)\in\{\left|\mu(n)\right|,\mu(n),\phi(n),\lambda(n)\}$

Published on 10 May 2026 - 13:27

score 152 · Answer 8 · 2026-05-10 14:05:40

152

Views

Equations involving arithmetic functions, totatives and even perfect numbers

Published on 10 May 2026 - 14:05

score 207 · Answer 9 · 2026-05-10 14:55:42

207

Views

For which $m$ does a primitive $m^{th}$ root of unity have degree $2$ over $\mathbb{Q}$?

Published on 10 May 2026 - 14:55

score 63 · Answer 10 · 2026-04-12 20:59:34

63

Views

Inequality involving summative totient function

Published on 12 Apr 2026 - 20:59

score 223 · Answer 11 · 2026-05-07 12:30:57

223

Views

Does exist any integer $n\geq 1$ satisfying $\varphi(12n)=\varphi(6n+5)$, where $\varphi(m)$ denotes the Euler's totient function?

Published on 07 May 2026 - 12:30

score 140 · Answer 12 · 2026-05-10 16:13:01

140

Views

Usage of $n=∑_{d|n}Φ(d)$

Published on 10 May 2026 - 16:13

score 494 · Answer 13 · 2026-05-07 07:40:52

494

Views

Find all $n$ such that i. $\phi(n)=\frac n2$, ii. $\phi(n)=4$.

Published on 07 May 2026 - 7:40

score 1k · Answer 14 · 2026-04-13 19:27:56

1k

Views

GCD sum using Euler's Totient

Published on 13 Apr 2026 - 19:27

score 141 · Answer 15 · 2026-05-10 16:12:58

141

Views

Congruence of a power with 1, $a^x \equiv 1\ mod \ (p^\alpha)$

Published on 10 May 2026 - 16:12

List Question

What is the probability for which :$\gcd ((\phi(n),n-1)=1 ) $ for integers?

On variations of Erdős squarefree conjecture: presentation and a question as a simple case

Let $\phi$ be Euler's totient function. Prove that $\phi(3n) = 3\phi(n)$ iff 3 divides n.

What is the explicit formula for $\Phi(x)=\sum\limits_{n=1}^x\phi(n)$?

Euler totient function equation: $\varphi(n)=42$

Show there are infinitely many positive integers $k$ such that $\phi(n)=k$ has exactly two solutions where $n$ is a positive integer

Questions on Convergence of Explicit Formulas for $f(x)=\sum\limits_{n=1}^x a(n)$ where $a(n)\in\{\left|\mu(n)\right|,\mu(n),\phi(n),\lambda(n)\}$

Equations involving arithmetic functions, totatives and even perfect numbers

For which $m$ does a primitive $m^{th}$ root of unity have degree $2$ over $\mathbb{Q}$?

Inequality involving summative totient function

Does exist any integer $n\geq 1$ satisfying $\varphi(12n)=\varphi(6n+5)$, where $\varphi(m)$ denotes the Euler's totient function?

Usage of $n=∑_{d|n}Φ(d)$

Find all $n$ such that i. $\phi(n)=\frac n2$, ii. $\phi(n)=4$.

GCD sum using Euler's Totient

Congruence of a power with 1, $a^x \equiv 1\ mod \ (p^\alpha)$

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