List questions from number-theory

Published on 09 Apr 2026 - 9:47

92

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Intersection of three events and a diophantine equation

Published on 15 Apr 2026 - 11:31

252

Views

Size of partial quotients in continued fraction expansion of $\sqrt{n}$

Published on 10 Apr 2026 - 11:16

64

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how to find three positive integers $\mathbf a, \mathbf b, \mathbf a+\mathbf b$ each can be write as a sum of two squares

Published on 16 Apr 2026 - 23:51

159

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How to compute $\prod_{1\le i\le n} \left(1-\frac{1}{2^i}\right)$

Published on 24 Apr 2026 - 6:36

149

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Prove that $\displaystyle \prod_{1\leq a<b\leq \frac{p-1}{2}}\,\left(a^2+b^2\right)\equiv \pm1\pmod{p}$ for a prime $p\equiv 3\pmod{4}$.

Published on 30 Apr 2026 - 2:07

73

Views

Is the maximum length of one irrational number within another finite?

Published on 14 Apr 2026 - 5:29

40

Views

A result on binary forms

Published on 15 Apr 2026 - 15:31

152

Views

Does the sequence $ (2\mathbb{N}+1 )^2 +4 $ find primes particularly well?

Published on 30 Apr 2026 - 2:06

119

Views

Solve $\pi(xn)=\frac{xn}{\frac{n}{\pi(n)}+\ln(x)}$

Published on 16 Apr 2026 - 3:22

184

Views

On the product $\prod_{1\leq a<b\leq \frac{p-1}{2}}\,\left(a^2+b^2\right)$, where $p$ is prime

Published on 15 Apr 2026 - 19:37

932

Views

Remainder on division with $22$

Published on 11 Apr 2026 - 14:41

730

Views

What is known about the $7x+1$ problem?

Published on 11 Apr 2026 - 17:37

44

Views

$V$ vector space over number field $K$. $L/K$ finite extension. lattice $M\subset V$. Then $M\otimes_{O_K} O_L\to V\otimes_K L$ is injection

Published on 14 Apr 2026 - 11:00

236

Views

$O(1)$ algorithm for Goldbach partitions, assuming $\pi(n)$ is known for all $0<n<2n$?

Published on 18 Apr 2026 - 12:48

List Question

How to prove the following floor function inequality?

Intersection of three events and a diophantine equation

Size of partial quotients in continued fraction expansion of $\sqrt{n}$

how to find three positive integers $\mathbf a, \mathbf b, \mathbf a+\mathbf b$ each can be write as a sum of two squares

How to compute $\prod_{1\le i\le n} \left(1-\frac{1}{2^i}\right)$

Prove that $\displaystyle \prod_{1\leq a<b\leq \frac{p-1}{2}}\,\left(a^2+b^2\right)\equiv \pm1\pmod{p}$ for a prime $p\equiv 3\pmod{4}$.

Is the maximum length of one irrational number within another finite?

A result on binary forms

Does the sequence $ (2\mathbb{N}+1 )^2 +4 $ find primes particularly well?

Solve $\pi(xn)=\frac{xn}{\frac{n}{\pi(n)}+\ln(x)}$

On the product $\prod_{1\leq a<b\leq \frac{p-1}{2}}\,\left(a^2+b^2\right)$, where $p$ is prime

Remainder on division with $22$

What is known about the $7x+1$ problem?

$V$ vector space over number field $K$. $L/K$ finite extension. lattice $M\subset V$. Then $M\otimes_{O_K} O_L\to V\otimes_K L$ is injection

$O(1)$ algorithm for Goldbach partitions, assuming $\pi(n)$ is known for all $0<n<2n$?

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