Question

Among $2n-1$ irrationals there are $x_1,\dots,x_n$ such that for rationals $a_i\ge0$ with $\sum_{i=1}^{n}a_i>0$, $\sum_{i=1}^{n}a_ix_i$ is irrational

score 111 · Answer 1 · 2026-03-23 14:18:12

111

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Among $2n-1$ irrationals there are $x_1,\dots,x_n$ such that for rationals $a_i\ge0$ with $\sum_{i=1}^{n}a_i>0$, $\sum_{i=1}^{n}a_ix_i$ is irrational

Published on 23 Mar 2026 - 14:18

score 165 · Answer 2 · 2026-03-24 13:27:23

165

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Is there an elegant Stern Brocot like way to generate all coprime triples?

Published on 24 Mar 2026 - 13:27

score 82 · Answer 3 · 2026-03-17 16:19:15

82

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Is there any pair of positive integers $ (x,n)$ for which :$e^{{e}^{{e}^{\cdots x}}}=2^{n}$?

Published on 17 Mar 2026 - 16:19

score 1.3k · Answer 4 · 2026-03-22 07:46:38

1.3k

Views

Elementary proof that the limit of $\sum_{i=1}^{\infty} \frac{1}{\operatorname{lcm}(1,2,...,i)}$ is irrational

Published on 22 Mar 2026 - 7:46

score 76 · Answer 5 · 2026-03-25 17:19:47

76

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Show that infinitely many $n$ exists for $c$ and $k$ that $|\sin(n^k)|<c$

Published on 25 Mar 2026 - 17:19

score 205 · Answer 6 · 2026-03-27 02:46:06

205

Views

How can you determine the accuracy of an equation to generate $\pi$

Published on 27 Mar 2026 - 2:46

score 89 · Answer 7 · 2026-03-17 08:34:54

89

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Why is :$\displaystyle {e}^\sqrt{2}$ is known to be transcedental number but ${\sqrt{2}}^ {e}$ is not known?

Published on 17 Mar 2026 - 8:34

score 66 · Answer 8 · 2018-02-01 19:07:30

66

Views

Find all $x \in \mathbb R$ such that $x + \sqrt{3}$ and $x^2 + \sqrt{3}$ are rational.

Published on 01 Feb 2018 - 19:07

score 108 · Answer 9 · 2026-03-25 10:34:52

108

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What is the contradiction of the statement $\forall r\in\mathbb{R}\ (\mathit{irrational}(r^3)\Rightarrow \mathit{irrational}(r))$?

Published on 25 Mar 2026 - 10:34

score 384 · Answer 10 · 2026-03-17 15:48:01

384

Views

Proving that $\sqrt{2}^{\sqrt{3}}$ is irrational

Published on 17 Mar 2026 - 15:48

score 2.6k · Answer 11 · 2026-03-25 03:18:57

2.6k

Views

Why can't imaginary numbers be irrational

Published on 25 Mar 2026 - 3:18

score 218 · Answer 12 · 2026-03-25 14:12:41

218

Views

Is there another proof about irrationality of $\sqrt{2}$ without using a contradiction?

Published on 25 Mar 2026 - 14:12

score 521 · Answer 13 · 2026-03-17 02:09:42

521

Views

Linear combination is not an integer

Published on 17 Mar 2026 - 2:09

score 536 · Answer 14 · 2026-03-16 22:45:39

536

Views

Simplification of Irrational Numbers

Published on 16 Mar 2026 - 22:45

score 105 · Answer 15 · 2026-03-25 19:46:13

105

Views

Linear transformation from irrationals to rationals with a constraint

Published on 25 Mar 2026 - 19:46

List Question

Among $2n-1$ irrationals there are $x_1,\dots,x_n$ such that for rationals $a_i\ge0$ with $\sum_{i=1}^{n}a_i>0$, $\sum_{i=1}^{n}a_ix_i$ is irrational

Is there an elegant Stern Brocot like way to generate all coprime triples?

Is there any pair of positive integers $ (x,n)$ for which :$e^{{e}^{{e}^{\cdots x}}}=2^{n}$?

Elementary proof that the limit of $\sum_{i=1}^{\infty} \frac{1}{\operatorname{lcm}(1,2,...,i)}$ is irrational

Show that infinitely many $n$ exists for $c$ and $k$ that $|\sin(n^k)|<c$

How can you determine the accuracy of an equation to generate $\pi$

Why is :$\displaystyle {e}^\sqrt{2}$ is known to be transcedental number but ${\sqrt{2}}^ {e}$ is not known?

Find all $x \in \mathbb R$ such that $x + \sqrt{3}$ and $x^2 + \sqrt{3}$ are rational.

What is the contradiction of the statement $\forall r\in\mathbb{R}\ (\mathit{irrational}(r^3)\Rightarrow \mathit{irrational}(r))$?

Proving that $\sqrt{2}^{\sqrt{3}}$ is irrational

Why can't imaginary numbers be irrational

Is there another proof about irrationality of $\sqrt{2}$ without using a contradiction?

Linear combination is not an integer

Simplification of Irrational Numbers

Linear transformation from irrationals to rationals with a constraint

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