Question

A congruence with the Euler's totient function and number of divisors function

score 152 · Answer 1 · 2026-03-24 07:36:54

152

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A congruence with the Euler's totient function and number of divisors function

Published on 24 Mar 2026 - 7:36

score 59 · Answer 2 · 2026-03-24 20:32:04

59

Views

Can we conclude that $n = m^2$ for some $m \in \mathbb N$?

Published on 24 Mar 2026 - 20:32

score 109 · Answer 3 · 2026-03-17 13:46:49

109

Views

Sophie Germain-like primes and Cunningham-like chains

Published on 17 Mar 2026 - 13:46

score 225 · Answer 4 · 2018-01-16 14:00:06

225

Views

Do there exist distinct prime numbers $p,q,r$ such that $\frac{p+q+r}{3}; \frac{p+q}2; \frac{r+q}2; \frac{p+r}2$ are prime numbers.

Published on 16 Jan 2018 - 14:00

score 482 · Answer 5 · 2026-03-24 15:55:15

482

Views

Prime coefficients in simultaneous equation. What are the integer solutions?

Published on 24 Mar 2026 - 15:55

score 132 · Answer 6 · 2018-01-17 20:51:12

132

Views

Has anyone seen my formula that approximates the number of primes up to n?

Published on 17 Jan 2018 - 20:51

score 116 · Answer 7 · 2026-03-24 13:51:34

116

Views

Fraction of two prime numbers

Published on 24 Mar 2026 - 13:51

score 141 · Answer 8 · 2026-03-22 12:21:08

141

Views

How can I prove $\frac{\zeta(k)}{\zeta(k+1)}=\sum\limits_{n=1}^{\infty}\frac{\varphi(n)}{n}\cdot\frac{1}{n^k}$?

Published on 22 Mar 2026 - 12:21

score 119 · Answer 9 · 2026-03-20 08:54:54

119

Views

A congruence involving Mersenne numbers

Published on 20 Mar 2026 - 8:54

score 159 · Answer 10 · 2026-03-22 14:00:38

159

Views

If $p$ and $p^2+2$ prime, then $p^3+2$ prime.

Published on 22 Mar 2026 - 14:00

score 225 · Answer 11 · 2026-03-21 01:53:40

225

Views

For any natural numbers a, b, c, d if ab = cd is it possible that a + b + c + d is prime number

Published on 21 Mar 2026 - 1:53

score 54 · Answer 12 · 2026-03-17 08:32:45

54

Views

Does converge $\sum_{n=2}^\infty\frac{1}{\varphi(p_n-2)-1+p_n}$, where $\varphi(n)$ is the Euler's totient function and $p_n$ the $n$th prime number?

Published on 17 Mar 2026 - 8:32

score 340 · Answer 13 · 2026-03-24 18:43:09

340

Views

Skewes' number, and the smallest $x$ such that $\pi(x) > \operatorname{li}(x) - \tfrac1n \operatorname{li}(x^{1/2})$?

Published on 24 Mar 2026 - 18:43

score 107 · Answer 14 · 2026-03-17 18:38:17

107

Views

On the behaviour of $\frac{1}{N}\sum_{k=1}^N\frac{\pi(\varphi(k)+N)}{\varphi(\pi(k)+N)}$ as $N\to\infty$

Published on 17 Mar 2026 - 18:38

score 178 · Answer 15 · 2026-03-19 18:04:57

178

Views

On the solutions of an equation involving the Euler's totient function that is solved by the primes of Rassias' conjecture

Published on 19 Mar 2026 - 18:04

List Question

A congruence with the Euler's totient function and number of divisors function

Can we conclude that $n = m^2$ for some $m \in \mathbb N$?

Sophie Germain-like primes and Cunningham-like chains

Do there exist distinct prime numbers $p,q,r$ such that $\frac{p+q+r}{3}; \frac{p+q}2; \frac{r+q}2; \frac{p+r}2$ are prime numbers.

Prime coefficients in simultaneous equation. What are the integer solutions?

Has anyone seen my formula that approximates the number of primes up to n?

Fraction of two prime numbers

How can I prove $\frac{\zeta(k)}{\zeta(k+1)}=\sum\limits_{n=1}^{\infty}\frac{\varphi(n)}{n}\cdot\frac{1}{n^k}$?

A congruence involving Mersenne numbers

If $p$ and $p^2+2$ prime, then $p^3+2$ prime.

For any natural numbers a, b, c, d if ab = cd is it possible that a + b + c + d is prime number

Does converge $\sum_{n=2}^\infty\frac{1}{\varphi(p_n-2)-1+p_n}$, where $\varphi(n)$ is the Euler's totient function and $p_n$ the $n$th prime number?

Skewes' number, and the smallest $x$ such that $\pi(x) > \operatorname{li}(x) - \tfrac1n \operatorname{li}(x^{1/2})$?

On the behaviour of $\frac{1}{N}\sum_{k=1}^N\frac{\pi(\varphi(k)+N)}{\varphi(\pi(k)+N)}$ as $N\to\infty$

On the solutions of an equation involving the Euler's totient function that is solved by the primes of Rassias' conjecture

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