Question

Conjecture: For any prime $n$, at least one of $2n^2-1$ , $2n^2+1$, or $\sqrt{2n^2-1}$ is prime.

score 96 · Answer 1 · 2024-02-05 09:30:09

96

Views

Conjecture: For any prime $n$, at least one of $2n^2-1$ , $2n^2+1$, or $\sqrt{2n^2-1}$ is prime.

Published on 05 Feb 2024 - 9:30

score 36 · Answer 2 · 2026-03-27 23:14:26

36

Views

True or false: In a 2D Poisson process, for every point $P$, there exists a convex $1000$-gon with Poisson points as vertices, that contains only $P$.

Published on 27 Mar 2026 - 23:14

score 315 · Answer 3 · 2024-02-10 10:52:58

315

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A conjecture on representing $\sum\limits_{k=0} ^m (-1)^ka^{m-k}b^k$ as sum of powers of $(a+b)$.

Published on 10 Feb 2024 - 10:52

score 48 · Answer 4 · 2026-02-23 10:06:16

48

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On the fractional parts of the roots of the Alternating Harmonic Numbers

Published on 23 Feb 2026 - 10:06

score 132 · Answer 5 · 2024-02-13 15:14:01

132

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(dis)proof of conjecture on square unit fractions

Published on 13 Feb 2024 - 15:14

score 791 · Answer 6 · 2024-02-19 04:49:02

791

Views

Is there a perfect group in which not every element is a commutator?

Published on 19 Feb 2024 - 4:49

score 54 · Answer 7 · 2024-03-04 13:27:35

54

Views

For any square-free $n \geq 1$ and $a \in \Bbb{Z}/n$ including $\gcd(a,n) \neq 1$, then in the list $a, a^2, a^3, \dots$ either $a$ or $a^2$ repeats?

Published on 04 Mar 2024 - 13:27

score 87 · Answer 8 · 2024-03-09 16:21:37

87

Views

Are there infinitely many primes that are a highly composite number $\pm 1$?

Published on 09 Mar 2024 - 16:21

score 58 · Answer 9 · 2026-02-23 06:38:03

58

Views

Conjecture about Proving Primality of Fermat numbers by Elliptic Curves technic

Published on 23 Feb 2026 - 6:38

score 57 · Answer 10 · 2024-03-15 14:49:06

57

Views

An extension of Brahmagupta's theorem.

Published on 15 Mar 2024 - 14:49

score 162 · Answer 11 · 2026-03-26 22:16:09

162

Views

Is $N=3\cdot 2^k+1$ prime if and only if $2^{N-1}\equiv 1 \pmod N$?

Published on 26 Mar 2026 - 22:16

score 36 · Answer 12 · 2024-03-30 03:01:23

36

Views

Is there any material on this simpler version of Littlewood's Conjecture?

Published on 30 Mar 2024 - 3:01

score 51 · Answer 13 · 2024-03-30 05:49:12

51

Views

Artin's conjecture on primitive roots for perfect powers

Published on 30 Mar 2024 - 5:49

score 64 · Answer 14 · 2024-03-30 20:18:11

64

Views

The Consecutive Composite Conjecture (Proof required)

Published on 30 Mar 2024 - 20:18

score 71 · Answer 15 · 2024-03-31 02:42:41

If $\lim\limits_{x\to\infty}\frac{f(x+1)-f(x)}{g(x+1)-g(x)}=l$ what are sufficient conditions to make $\lim\limits_{x\to\infty}\frac{f(x)}{g(x)}=l$?

List Question

Conjecture: For any prime $n$, at least one of $2n^2-1$ , $2n^2+1$, or $\sqrt{2n^2-1}$ is prime.

True or false: In a 2D Poisson process, for every point $P$, there exists a convex $1000$-gon with Poisson points as vertices, that contains only $P$.

A conjecture on representing $\sum\limits_{k=0} ^m (-1)^ka^{m-k}b^k$ as sum of powers of $(a+b)$.

On the fractional parts of the roots of the Alternating Harmonic Numbers

(dis)proof of conjecture on square unit fractions

Is there a perfect group in which not every element is a commutator?

For any square-free $n \geq 1$ and $a \in \Bbb{Z}/n$ including $\gcd(a,n) \neq 1$, then in the list $a, a^2, a^3, \dots$ either $a$ or $a^2$ repeats?

Are there infinitely many primes that are a highly composite number $\pm 1$?

Conjecture about Proving Primality of Fermat numbers by Elliptic Curves technic

An extension of Brahmagupta's theorem.

Is $N=3\cdot 2^k+1$ prime if and only if $2^{N-1}\equiv 1 \pmod N$?

Is there any material on this simpler version of Littlewood's Conjecture?

Artin's conjecture on primitive roots for perfect powers

The Consecutive Composite Conjecture (Proof required)

If $\lim\limits_{x\to\infty}\frac{f(x+1)-f(x)}{g(x+1)-g(x)}=l$ what are sufficient conditions to make $\lim\limits_{x\to\infty}\frac{f(x)}{g(x)}=l$?

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