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 121 · Answer 1 · 2026-05-07 20:32:34

121

Views

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 07 May 2026 - 20:32

score 173 · Answer 2 · 2026-05-07 12:54:00

173

Views

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

Published on 07 May 2026 - 12:54

score 91 · Answer 3 · 2026-05-05 06:19:14

91

Views

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

Published on 05 May 2026 - 6:19

score 1.3k · Answer 4 · 2026-05-13 18:00:13

1.3k

Views

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

Published on 13 May 2026 - 18:00

score 81 · Answer 5 · 2026-05-11 09:33:36

81

Views

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

Published on 11 May 2026 - 9:33

score 212 · Answer 6 · 2026-05-03 01:51:18

212

Views

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

Published on 03 May 2026 - 1:51

score 98 · Answer 7 · 2026-05-05 03:27:16

98

Views

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

Published on 05 May 2026 - 3:27

score 71 · Answer 8 · 2026-04-29 12:51:45

71

Views

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

Published on 29 Apr 2026 - 12:51

score 111 · Answer 9 · 2026-05-10 23:37:56

111

Views

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

Published on 10 May 2026 - 23:37

score 388 · Answer 10 · 2026-04-29 12:51:29

388

Views

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

Published on 29 Apr 2026 - 12:51

score 2.6k · Answer 11 · 2026-05-10 19:12:49

2.6k

Views

Why can't imaginary numbers be irrational

Published on 10 May 2026 - 19:12

score 223 · Answer 12 · 2026-05-10 12:33:35

223

Views

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

Published on 10 May 2026 - 12:33

score 526 · Answer 13 · 2026-04-29 12:51:22

526

Views

Linear combination is not an integer

Published on 29 Apr 2026 - 12:51

score 542 · Answer 14 · 2026-04-29 12:51:50

542

Views

Simplification of Irrational Numbers

Published on 29 Apr 2026 - 12:51

score 113 · Answer 15 · 2026-05-10 12:33:28

113

Views

Linear transformation from irrationals to rationals with a constraint

Published on 10 May 2026 - 12:33

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

Trending Questions

Popular # Hahtags

Popular Questions