Question

Existence of positive integers $m,k$ such that $2^m > k\alpha > 2^m - 1$ for fixed irrational number $\alpha$.

score 302 · Answer 1 · 2017-02-26 23:18:17

302

Views

Existence of positive integers $m,k$ such that $2^m > k\alpha > 2^m - 1$ for fixed irrational number $\alpha$.

Published on 26 Feb 2017 - 23:18

score 66 · Answer 2 · 2017-03-01 12:44:41

66

Views

How to prove that the distance of $n\sqrt{3}$ to an integer is larger than $\frac{1}{3n\sqrt{3}}$?

Published on 01 Mar 2017 - 12:44

score 115 · Answer 3 · 2017-03-05 09:09:40

115

Views

Extension of 1991 IMO question

Published on 05 Mar 2017 - 9:09

score 297 · Answer 4 · 2017-03-12 05:23:24

297

Views

Is the LLL algorithm only applicable with integers?

Published on 12 Mar 2017 - 5:23

score 172 · Answer 5 · 2017-03-14 14:07:27

172

Views

Simultaneous Diophantine approximation in the non-generic case

Published on 14 Mar 2017 - 14:07

score 734 · Answer 6 · 2017-03-16 20:08:23

734

Views

Approximating a real number by a fraction from one side

Published on 16 Mar 2017 - 20:08

score 64 · Answer 7 · 2026-03-25 21:16:20

64

Views

Almost diophantine equations?

Published on 25 Mar 2026 - 21:16

score 402 · Answer 8 · 2017-03-22 12:00:38

402

Views

Simultaneous Diophantine approximation: multiple solutions required

Published on 22 Mar 2017 - 12:00

score 449 · Answer 9 · 2017-03-30 23:47:36

449

Views

Irrationality measure of $\alpha+\beta$, $\alpha\beta$

Published on 30 Mar 2017 - 23:47

score 645 · Answer 10 · 2017-04-03 22:22:12

645

Views

Diophantine approximation - Closest lattice point to a line (2d)

Published on 03 Apr 2017 - 22:22

score 82 · Answer 11 · 2017-04-04 13:28:18

82

Views

How to find this Littlewood conjecture estimate?

Published on 04 Apr 2017 - 13:28

score 25 · Answer 12 · 2023-02-01 10:31:26

25

Views

Orbits Of $SL_d(\mathbb{Z})$ on non rational and non - irrational points in the $d$ - Dimensional Torus

Published on 01 Feb 2023 - 10:31

score 32 · Answer 13 · 2023-02-12 10:56:15

32

Views

Three or more points moving on a circle and a convergent subsequence

Published on 12 Feb 2023 - 10:56

score 75 · Answer 14 · 2023-02-18 17:45:22

75

Views

Let $x\in\mathbb{R}.$ For each $n,$ define $x_n:=\min_{k\in\mathbb{Z}}\lvert\frac{k}{n}-x \rvert.$ For which values of $x$ does $\sum x_n$ converge?

Published on 18 Feb 2023 - 17:45

score 344 · Answer 15 · 2023-02-20 23:00:16

344

Views

Help understanding steps to prove Dirichlet's approximation theorem

Published on 20 Feb 2023 - 23:00

List Question

Existence of positive integers $m,k$ such that $2^m > k\alpha > 2^m - 1$ for fixed irrational number $\alpha$.

How to prove that the distance of $n\sqrt{3}$ to an integer is larger than $\frac{1}{3n\sqrt{3}}$?

Extension of 1991 IMO question

Is the LLL algorithm only applicable with integers?

Simultaneous Diophantine approximation in the non-generic case

Approximating a real number by a fraction from one side

Almost diophantine equations?

Simultaneous Diophantine approximation: multiple solutions required

Irrationality measure of $\alpha+\beta$, $\alpha\beta$

Diophantine approximation - Closest lattice point to a line (2d)

How to find this Littlewood conjecture estimate?

Orbits Of $SL_d(\mathbb{Z})$ on non rational and non - irrational points in the $d$ - Dimensional Torus

Three or more points moving on a circle and a convergent subsequence

Let $x\in\mathbb{R}.$ For each $n,$ define $x_n:=\min_{k\in\mathbb{Z}}\lvert\frac{k}{n}-x \rvert.$ For which values of $x$ does $\sum x_n$ converge?

Help understanding steps to prove Dirichlet's approximation theorem

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