Question

Is $\ a^b+b^a\ $ transcendental if $\ a^b\ $ and $\ b^a\ $ are?

score 93 · Answer 1 · 2026-03-25 01:28:32

93

Views

Is $\ a^b+b^a\ $ transcendental if $\ a^b\ $ and $\ b^a\ $ are?

Published on 25 Mar 2026 - 1:28

score 160 · Answer 2 · 2026-03-25 08:23:35

160

Views

Algebraic functions on transcendental numbers

Published on 25 Mar 2026 - 8:23

score 91 · Answer 3 · 2026-03-24 20:32:58

91

Views

$n^\pi$ and $n^e$ for positive integer $n\ge2$

Published on 24 Mar 2026 - 20:32

score 242 · Answer 4 · 2026-02-23 04:58:21

242

Views

Show that if $\beta \in E$ is algebraic over $F(\alpha)$, then there is a nonzero polynomial $f(x,y) \in F[x,y]$ such that $f(\alpha, \beta)=0$.

Published on 23 Feb 2026 - 4:58

score 12.8k · Answer 5 · 2026-03-25 18:47:16

12.8k

Views

e is irrational

Published on 25 Mar 2026 - 18:47

score 51 · Answer 6 · 2026-03-25 17:38:08

51

Views

Borel's result on transcendence measure

Published on 25 Mar 2026 - 17:38

score 174 · Answer 7 · 2026-03-25 04:11:19

174

Views

How to prove this: If $t$ is a transcendental number, then $5t^{4}+8t+3$ is also transcendental?

Published on 25 Mar 2026 - 4:11

score 770 · Answer 8 · 2026-03-25 01:45:34

770

Views

What would change in mathematics if we knew $\pi+e$ is rational?

Published on 25 Mar 2026 - 1:45

score 2.1k · Answer 9 · 2026-03-25 09:05:07

2.1k

Views

Is $\log 2\pi$ rational?

Published on 25 Mar 2026 - 9:05

score 181 · Answer 10 · 2026-03-24 01:12:06

181

Views

Let $t$ be a transcendental number. Prove that the set $\{(a+bt) \mid a,b \in \mathbb{Q}\}$ is not a number field.

Published on 24 Mar 2026 - 1:12

score 131 · Answer 11 · 2026-03-25 09:17:55

131

Views

The smallest class of numbers closed under addition, multiplication, and exponentiation

Published on 25 Mar 2026 - 9:17

score 65 · Answer 12 · 2026-03-24 23:05:51

65

Views

How to show $\{a^n \bmod \alpha\}_{n \in \mathbb{N}}$ is dense in $[0,\alpha]$ if $a > 1$ is trancendental over ${\mathbb Q}[\alpha]$

Published on 24 Mar 2026 - 23:05

score 1.3k · Answer 13 · 2026-03-25 02:51:56

1.3k

Views

2.71828. And then another 1828.

Published on 25 Mar 2026 - 2:51

score 287 · Answer 14 · 2026-03-25 01:38:22

287

Views

Question about $e^{e^{e^e}}$

Published on 25 Mar 2026 - 1:38

score 149 · Answer 15 · 2026-03-25 03:28:33

149

Views

Prove that if $t \in T$ and $q \in Q$, but $q \neq 0$ then $qt \in T$ (where $T$ = transcendental numbers)

Published on 25 Mar 2026 - 3:28

List Question

Is $\ a^b+b^a\ $ transcendental if $\ a^b\ $ and $\ b^a\ $ are?

Algebraic functions on transcendental numbers

$n^\pi$ and $n^e$ for positive integer $n\ge2$

Show that if $\beta \in E$ is algebraic over $F(\alpha)$, then there is a nonzero polynomial $f(x,y) \in F[x,y]$ such that $f(\alpha, \beta)=0$.

e is irrational

Borel's result on transcendence measure

How to prove this: If $t$ is a transcendental number, then $5t^{4}+8t+3$ is also transcendental?

What would change in mathematics if we knew $\pi+e$ is rational?

Is $\log 2\pi$ rational?

Let $t$ be a transcendental number. Prove that the set $\{(a+bt) \mid a,b \in \mathbb{Q}\}$ is not a number field.

The smallest class of numbers closed under addition, multiplication, and exponentiation

How to show $\{a^n \bmod \alpha\}_{n \in \mathbb{N}}$ is dense in $[0,\alpha]$ if $a > 1$ is trancendental over ${\mathbb Q}[\alpha]$

2.71828. And then another 1828.

Question about $e^{e^{e^e}}$

Prove that if $t \in T$ and $q \in Q$, but $q \neq 0$ then $qt \in T$ (where $T$ = transcendental numbers)

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