Question

How can you prove or disprove that half of all natural numbers can be expressed as the sum of three squares minus the product of their roots?

score 402 · Answer 1 · 2023-08-24 00:42:42

402

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How can you prove or disprove that half of all natural numbers can be expressed as the sum of three squares minus the product of their roots?

Published on 24 Aug 2023 - 0:42

score 100 · Answer 2 · 2026-02-23 06:35:00

100

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Conjecture about non-squarefree numbers.

Published on 23 Feb 2026 - 6:35

score 43 · Answer 3 · 2023-08-28 17:37:47

43

Views

Computing the least common multiple of the numbers 1 through n for incremental n

Published on 28 Aug 2023 - 17:37

score 200 · Answer 4 · 2023-08-30 17:37:42

200

Views

Possible connection between prime numbers in binary and $\pi$

Published on 30 Aug 2023 - 17:37

score 37 · Answer 5 · 2023-09-06 16:01:15

37

Views

Deterministically finding $g$ such that $f(g(x)) \ge x$?

Published on 06 Sep 2023 - 16:01

score 797 · Answer 6 · 2023-09-09 07:32:14

797

Views

Conjecture: If matrix $M$ has entries (left to right, then top to botom) $\sin 1,\sin 2,\sin 3,\dots,\sin (n^2)$, where $n\ge 3$, then $\det M = 0$.

Published on 09 Sep 2023 - 7:32

score 93 · Answer 7 · 2026-03-25 23:37:10

93

Views

A Number-theoretic Generalization of the Union-closed Sets Conjecture

Published on 25 Mar 2026 - 23:37

score 207 · Answer 8 · 2026-03-26 13:00:45

207

Views

A conjecture for the golden ration via continued fraction $\phi=\frac{1+\sqrt{5}}{2}$

Published on 26 Mar 2026 - 13:00

score 332 · Answer 9 · 2023-10-06 12:11:56

332

Views

Conjecture: If $a_1\in\mathbb{Z}$ and $a_n=\sec (a_{n-1})$ then the proportion of positive terms approaches $\frac{1}{\sqrt{2\pi}}$ as $n\to\infty$.

Published on 06 Oct 2023 - 12:11

score 53 · Answer 10 · 2023-10-15 23:38:28

53

Views

How do I find the focal distance?

Published on 15 Oct 2023 - 23:38

score 94 · Answer 11 · 2023-10-16 07:45:32

94

Views

Why don't prime counting approximations work for Brocard's conjecture?

Published on 16 Oct 2023 - 7:45

score 137 · Answer 12 · 2026-03-28 00:00:11

137

Views

Conjecture: If $f(x)=\prod\limits_{k=1}^n(x-k)$ then $\lim\limits_{n\to\infty}\frac1n [\text{largest root of $f(x)=f'(x)$}]=\frac{e}{e-1}$.

Published on 28 Mar 2026 - 0:00

score 329 · Answer 13 · 2023-10-21 05:36:34

329

Views

Conjecture for Integrals of the Form $\int_{0}^{1}\frac{\ln^n\left(1-x^{2}\right)}{1+x}dx$

Published on 21 Oct 2023 - 5:36

score 229 · Answer 14 · 2023-10-22 08:12:32

229

Views

Sendov's conjecture and squaring polynomial

Published on 22 Oct 2023 - 8:12

score 42 · Answer 15 · 2023-10-22 15:05:55

42

Views

Are there any general results that relate the amount of solutions to a diophantine equations to the average growth rate of such solutions?

Published on 22 Oct 2023 - 15:05

List Question

How can you prove or disprove that half of all natural numbers can be expressed as the sum of three squares minus the product of their roots?

Conjecture about non-squarefree numbers.

Computing the least common multiple of the numbers 1 through n for incremental n

Possible connection between prime numbers in binary and $\pi$

Deterministically finding $g$ such that $f(g(x)) \ge x$?

Conjecture: If matrix $M$ has entries (left to right, then top to botom) $\sin 1,\sin 2,\sin 3,\dots,\sin (n^2)$, where $n\ge 3$, then $\det M = 0$.

A Number-theoretic Generalization of the Union-closed Sets Conjecture

A conjecture for the golden ration via continued fraction $\phi=\frac{1+\sqrt{5}}{2}$

Conjecture: If $a_1\in\mathbb{Z}$ and $a_n=\sec (a_{n-1})$ then the proportion of positive terms approaches $\frac{1}{\sqrt{2\pi}}$ as $n\to\infty$.

How do I find the focal distance?

Why don't prime counting approximations work for Brocard's conjecture?

Conjecture: If $f(x)=\prod\limits_{k=1}^n(x-k)$ then $\lim\limits_{n\to\infty}\frac1n [\text{largest root of $f(x)=f'(x)$}]=\frac{e}{e-1}$.

Conjecture for Integrals of the Form $\int_{0}^{1}\frac{\ln^n\left(1-x^{2}\right)}{1+x}dx$

Sendov's conjecture and squaring polynomial

Are there any general results that relate the amount of solutions to a diophantine equations to the average growth rate of such solutions?

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