List questions from diophantine-approximation

Published on 03 Aug 2011 - 5:03

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For what $\lambda$ does the sequence $\left\{ \frac{k}{2\lambda} \right\}$ converge?

Published on 26 Sep 2011 - 3:17

23.1k

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Proving that $m+n\sqrt{2}$ is dense in $\mathbb R$

Published on 17 Oct 2011 - 5:40

1.1k

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When is a sequence $(x_n) \subset [0,1]$ dense in $[0,1]$?

Published on 25 Mar 2026 - 23:36

1.1k

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Is there any real number except 1 which is equal to its own irrationality measure?

Published on 13 Dec 2011 - 19:54

248

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badly approximated numbers on the real line form a meagre set

Published on 09 Feb 2012 - 16:15

193

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Is an integer in the interval $\left[\small {3^n+1 \over 2^n+1}\lt {3^n \over 2^n} \lt{3^n-1 \over 2^n-1}\right] $ for some $\small n>1$?

Published on 12 Feb 2012 - 13:01

792

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Is there a 'far' irrational number?

Published on 14 Feb 2012 - 18:02

187

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Do best lower approximations of a quadratic irrational always form a linear recurrence sequence?

Published on 23 Feb 2012 - 17:58

394

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Solutions of $x^2 + 119 = 15 \cdot 2^n$ without trial and error

Published on 24 Mar 2012 - 6:58

194

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Constructive proof need to know the solutions of the equations

Published on 26 Mar 2012 - 6:37

1.2k

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Discrete rational rotations on the two dimensional torus

Published on 06 Jun 2012 - 20:15

601

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For a trigonometric polynomial $P$, can $\lim \limits_{n \to \infty} P(n^2) = 0$ without $P(n^2) = 0$?

Published on 06 Jul 2012 - 23:08

153

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prove existence of integers $a,q$ which satisfy the following inequality

Published on 02 Aug 2012 - 9:22

381

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Why does the set of real numbers with irrationality measure $\gt 2$ have zero measure?

Published on 20 Aug 2012 - 23:23

List Question

Motivation of irrationality measure

For what $\lambda$ does the sequence $\left\{ \frac{k}{2\lambda} \right\}$ converge?

Proving that $m+n\sqrt{2}$ is dense in $\mathbb R$

When is a sequence $(x_n) \subset [0,1]$ dense in $[0,1]$?

Is there any real number except 1 which is equal to its own irrationality measure?

badly approximated numbers on the real line form a meagre set

Is an integer in the interval $\left[\small {3^n+1 \over 2^n+1}\lt {3^n \over 2^n} \lt{3^n-1 \over 2^n-1}\right] $ for some $\small n>1$?

Is there a 'far' irrational number?

Do best lower approximations of a quadratic irrational always form a linear recurrence sequence?

Solutions of $x^2 + 119 = 15 \cdot 2^n$ without trial and error

Constructive proof need to know the solutions of the equations

Discrete rational rotations on the two dimensional torus

For a trigonometric polynomial $P$, can $\lim \limits_{n \to \infty} P(n^2) = 0$ without $P(n^2) = 0$?

prove existence of integers $a,q$ which satisfy the following inequality

Why does the set of real numbers with irrationality measure $\gt 2$ have zero measure?

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