Question

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

score 163 · Answer 1 · 2026-05-07 16:39:29

163

Views

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

Published on 07 May 2026 - 16:39

score 65 · Answer 2 · 2026-04-29 12:25:13

65

Views

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

Published on 29 Apr 2026 - 12:25

score 114 · Answer 3 · 2026-04-29 12:46:12

114

Views

Sophie Germain-like primes and Cunningham-like chains

Published on 29 Apr 2026 - 12:46

score 231 · Answer 4 · 2026-04-29 12:46:10

231

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 29 Apr 2026 - 12:46

score 486 · Answer 5 · 2026-04-29 12:46:13

486

Views

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

Published on 29 Apr 2026 - 12:46

score 138 · Answer 6 · 2026-04-29 12:46:09

138

Views

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

Published on 29 Apr 2026 - 12:46

score 122 · Answer 7 · 2026-04-29 12:18:17

122

Views

Fraction of two prime numbers

Published on 29 Apr 2026 - 12:18

score 147 · Answer 8 · 2026-05-02 18:46:16

147

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 02 May 2026 - 18:46

score 128 · Answer 9 · 2026-04-29 12:08:05

128

Views

A congruence involving Mersenne numbers

Published on 29 Apr 2026 - 12:08

score 162 · Answer 10 · 2026-04-29 12:45:44

162

Views

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

Published on 29 Apr 2026 - 12:45

score 233 · Answer 11 · 2026-04-29 12:06:36

233

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 29 Apr 2026 - 12:06

score 64 · Answer 12 · 2026-05-07 07:41:32

64

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 07 May 2026 - 7:41

score 349 · Answer 13 · 2026-05-07 10:14:11

349

Views

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

Published on 07 May 2026 - 10:14

score 118 · Answer 14 · 2026-04-29 12:16:15

118

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 29 Apr 2026 - 12:16

score 188 · Answer 15 · 2026-05-07 14:36:28

188

Views

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

Published on 07 May 2026 - 14:36

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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