Question

Is the value of $\log_27$ a rational number?

score 213 · Answer 1 · 2016-05-23 15:06:25

213

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Is the value of $\log_27$ a rational number?

Published on 23 May 2016 - 15:06

score 280 · Answer 2 · 2016-05-26 02:29:25

280

Views

Show that there are at most two rational points on $(x - a)^2 + (y - b)^2 = r^2$ for $a, b$ irrational.

Published on 26 May 2016 - 2:29

score 640 · Answer 3 · 2026-04-01 03:45:16

640

Views

For irrational real number $r$, find $n \in \mathbb{Z}$ such that $|nr - [nr]| < 10^{-10}$.

Published on 01 Apr 2026 - 3:45

score 6.5k · Answer 4 · 2026-03-28 05:38:55

6.5k

Views

Prove at least one of $\pi+e$, $\pi e$ is transcendental.

Published on 28 Mar 2026 - 5:38

score 108 · Answer 5 · 2016-05-31 12:54:00

108

Views

Which elements of $\mathbb{R}$ make sense as representatives for cosets of $\mathbb{Q}$ in the group $\mathbb{R/Q}$

Published on 31 May 2016 - 12:54

score 7.5k · Answer 6 · 2016-05-31 22:31:39

7.5k

Views

when product of irrational numbers = rational number?

Published on 31 May 2016 - 22:31

score 99 · Answer 7 · 2016-06-01 16:50:56

99

Views

Are all hypotenuses irrational if the shorter sides are integers?

Published on 01 Jun 2016 - 16:50

score 126 · Answer 8 · 2016-06-02 09:51:24

126

Views

Is there any $\alpha$ for which $e^{\alpha}$ is an integer?

Published on 02 Jun 2016 - 9:51

score 50 · Answer 9 · 2016-06-05 15:23:25

50

Views

A sum of irrational numbers ending rational

Published on 05 Jun 2016 - 15:23

score 91 · Answer 10 · 2026-04-03 16:53:44

91

Views

Can we apply binomial theorem for $\quad(a+b)^\ell\quad$ if $\ell\;$ irrational.

Published on 03 Apr 2026 - 16:53

score 637 · Answer 11 · 2016-06-07 13:51:52

637

Views

Prove $2^{1/2}+3^{1/3}$ is irrational using Galois theory.

Published on 07 Jun 2016 - 13:51

score 191 · Answer 12 · 2016-06-08 19:01:31

191

Views

Proof that $\sqrt[n]{a+1}$ and $\sqrt[n]{a-1}$ cannot be both rationals

Published on 08 Jun 2016 - 19:01

score 201 · Answer 13 · 2016-06-10 03:20:04

201

Views

Polynomial taking irrationals to irrationals

Published on 10 Jun 2016 - 3:20

score 65 · Answer 14 · 2016-06-10 17:25:16

65

Views

Proving by contradiction (6/9)

Published on 10 Jun 2016 - 17:25

score 3.9k · Answer 15 · 2026-03-28 01:07:15

3.9k

Views

Visual representation of the fact that there are more irrational than rational numbers.

Published on 28 Mar 2026 - 1:07

List Question

Is the value of $\log_27$ a rational number?

Show that there are at most two rational points on $(x - a)^2 + (y - b)^2 = r^2$ for $a, b$ irrational.

For irrational real number $r$, find $n \in \mathbb{Z}$ such that $|nr - [nr]| < 10^{-10}$.

Prove at least one of $\pi+e$, $\pi e$ is transcendental.

Which elements of $\mathbb{R}$ make sense as representatives for cosets of $\mathbb{Q}$ in the group $\mathbb{R/Q}$

when product of irrational numbers = rational number?

Are all hypotenuses irrational if the shorter sides are integers?

Is there any $\alpha$ for which $e^{\alpha}$ is an integer?

A sum of irrational numbers ending rational

Can we apply binomial theorem for $\quad(a+b)^\ell\quad$ if $\ell\;$ irrational.

Prove $2^{1/2}+3^{1/3}$ is irrational using Galois theory.

Proof that $\sqrt[n]{a+1}$ and $\sqrt[n]{a-1}$ cannot be both rationals

Polynomial taking irrationals to irrationals

Proving by contradiction (6/9)

Visual representation of the fact that there are more irrational than rational numbers.

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