List questions from diophantine-approximation

Published on 22 Mar 2026 - 12:00

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Show that $x^2 + y^2 = 3$ has no rational points

Published on 20 Mar 2026 - 2:19

173

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Any suggestions on how to compute $\limsup |\cos n|^{n^2}$?

Published on 21 Mar 2026 - 19:49

648

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Exploiting a Diophantine approximation of $\pi^4$ into giving a series of rationals for $\pi^4$

Published on 21 Mar 2026 - 21:06

83

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Motivation behind proof of Behrend's theorem on size of AP free subset

Published on 21 Mar 2026 - 16:13

66

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Why we get inequality form an equation?

Published on 22 Mar 2026 - 9:08

140

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Finding the minimal value of a $4\times 4$ determinant

Published on 21 Mar 2026 - 21:08

134

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A linear form can not be too small on integer points

Published on 22 Mar 2026 - 14:45

100

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Finding a minima for a linear form with integer coefficients

Published on 21 Mar 2026 - 12:54

139

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How many integer solutions are there to $x^4+y^4-x^2y^2=n$. Is there a generating function for this?

Published on 25 Mar 2026 - 1:23

123

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Approximating a real arbitrarily well by $Z$-linear combination of two reals having irrational ratio.

Published on 21 Mar 2026 - 2:26

162

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Siegel's lemma for arbitary number field.

Published on 22 Mar 2026 - 19:00

145

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Does $lcm\{1,2,...,n\} = \prod_{p\leq n, p\in\mathbb{P}}p^{\lceil \frac{log(n)}{log(p)}\rceil}$?

Published on 21 Mar 2026 - 21:02

160

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Irrationality measure of $\frac{\ln{3}}{\ln{2}}$.

Published on 21 Mar 2026 - 23:09

129

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$0<|\sqrt a-\sqrt[3]b|<\epsilon$ for $a,b\in\Bbb Z_+$

Published on 21 Mar 2026 - 18:05

List Question

Can we remove the absolute value when doing Diophantine Approximation?

Show that $x^2 + y^2 = 3$ has no rational points

Any suggestions on how to compute $\limsup |\cos n|^{n^2}$?

Exploiting a Diophantine approximation of $\pi^4$ into giving a series of rationals for $\pi^4$

Motivation behind proof of Behrend's theorem on size of AP free subset

Why we get inequality form an equation?

Finding the minimal value of a $4\times 4$ determinant

A linear form can not be too small on integer points

Finding a minima for a linear form with integer coefficients

How many integer solutions are there to $x^4+y^4-x^2y^2=n$. Is there a generating function for this?

Approximating a real arbitrarily well by $Z$-linear combination of two reals having irrational ratio.

Siegel's lemma for arbitary number field.

Does $lcm\{1,2,...,n\} = \prod_{p\leq n, p\in\mathbb{P}}p^{\lceil \frac{log(n)}{log(p)}\rceil}$?

Irrationality measure of $\frac{\ln{3}}{\ln{2}}$.

$0<|\sqrt a-\sqrt[3]b|<\epsilon$ for $a,b\in\Bbb Z_+$

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