Question

On a conjecture that if $2\left(p_n+p_{n-1}\right)\equiv -1\pmod {n^2}$ then $n=11$ only.

score 101 · Answer 1 · 2018-05-06 05:26:12

101

Views

On a conjecture that if $2\left(p_n+p_{n-1}\right)\equiv -1\pmod {n^2}$ then $n=11$ only.

Published on 06 May 2018 - 5:26

score 256 · Answer 2 · 2018-05-07 08:40:51

256

Views

Is $387420547$ another counter example to John H. Conway's Problem $5$?

Published on 07 May 2018 - 8:40

score 27 · Answer 3 · 2026-03-25 03:01:14

27

Views

Questions regarding equations that involve arithmetic functions, and odd integers being deficient or perfect

Published on 25 Mar 2026 - 3:01

score 81 · Answer 4 · 2026-03-25 04:42:57

81

Views

Confirmation of Proof: $\pi_n + p_a + p_b \geqslant \sum_{i=1}^4 x_i$.

Published on 25 Mar 2026 - 4:42

score 201 · Answer 5 · 2026-03-25 03:07:31

201

Views

Do odd numbers $n$ satisfying $\gcd(n, \sigma(n)) > \sqrt{n}$ have a special form?

Published on 25 Mar 2026 - 3:07

score 91 · Answer 6 · 2026-03-25 06:04:33

91

Views

Is $N^n(p_n\#)-p_n\#$ always prime for all $n\in\mathbb{N}_{>1}$?

Published on 25 Mar 2026 - 6:04

score 251 · Answer 7 · 2018-05-22 14:09:25

251

Views

Is this integral $\int_0^\infty\frac{\cos(a x+ 2b \arctan x)}{x^2+1}dx$ exactly zero when $b\in\mathbb{N}$?

Published on 22 May 2018 - 14:09

score 697 · Answer 8 · 2026-03-25 06:04:06

697

Views

Is it true that $2^{2^{n}}$ always ends in the digit $6$?

Published on 25 Mar 2026 - 6:04

score 788 · Answer 9 · 2026-03-22 23:22:15

788

Views

Is my proof correct on how $k$ must be a power of $2$? Are there other proofs?

Published on 22 Mar 2026 - 23:22

score 414 · Answer 10 · 2018-05-25 08:18:11

414

Views

Does the prime sequence satisfy $p_n+p_m \le p_{n+m} < p_n p_m$?

Published on 25 May 2018 - 8:18

score 162 · Answer 11 · 2018-05-25 09:26:59

162

Views

Conjectured inequality: $\frac{p_{2n+1}-1}{2}\geqslant p_{n+1}+2(n+1)^{2/(n-1)}+\frac12\log_{4}^2(n-6)\qquad(n>6)$

Published on 25 May 2018 - 9:26

score 85 · Answer 12 · 2018-05-25 13:11:53

85

Views

Is $\sum_{i=1}^{n-1}i^{n-1}\equiv -1\pmod {2n}\Leftrightarrow \text{$n$ is prime }\equiv 3\pmod 4$?

Published on 25 May 2018 - 13:11

score 951 · Answer 13 · 2018-05-26 09:39:37

951

Views

Conways 99 graph problem

Published on 26 May 2018 - 9:39

score 90 · Answer 14 · 2026-03-23 11:14:37

90

Views

On a conjecture that $P_n^{\,2}+5^2+2^k=(P_n-1)^2+l^2$.

Published on 23 Mar 2026 - 11:14

score 217 · Answer 15 · 2018-05-27 07:03:15

217

Views

Approaches to Brocard's problem

Published on 27 May 2018 - 7:03

List Question

On a conjecture that if $2\left(p_n+p_{n-1}\right)\equiv -1\pmod {n^2}$ then $n=11$ only.

Is $387420547$ another counter example to John H. Conway's Problem $5$?

Questions regarding equations that involve arithmetic functions, and odd integers being deficient or perfect

Confirmation of Proof: $\pi_n + p_a + p_b \geqslant \sum_{i=1}^4 x_i$.

Do odd numbers $n$ satisfying $\gcd(n, \sigma(n)) > \sqrt{n}$ have a special form?

Is $N^n(p_n\#)-p_n\#$ always prime for all $n\in\mathbb{N}_{>1}$?

Is this integral $\int_0^\infty\frac{\cos(a x+ 2b \arctan x)}{x^2+1}dx$ exactly zero when $b\in\mathbb{N}$?

Is it true that $2^{2^{n}}$ always ends in the digit $6$?

Is my proof correct on how $k$ must be a power of $2$? Are there other proofs?

Does the prime sequence satisfy $p_n+p_m \le p_{n+m} < p_n p_m$?

Conjectured inequality: $\frac{p_{2n+1}-1}{2}\geqslant p_{n+1}+2(n+1)^{2/(n-1)}+\frac12\log_{4}^2(n-6)\qquad(n>6)$

Is $\sum_{i=1}^{n-1}i^{n-1}\equiv -1\pmod {2n}\Leftrightarrow \text{$n$ is prime }\equiv 3\pmod 4$?

Conways 99 graph problem

On a conjecture that $P_n^{\,2}+5^2+2^k=(P_n-1)^2+l^2$.

Approaches to Brocard's problem

Trending Questions

Popular # Hahtags

Popular Questions