Question

Does $6^x+3^x=10$ have an solution that is an algebraic number?

score 163 · Answer 1 · 2026-03-24 19:14:12

163

Views

Does $6^x+3^x=10$ have an solution that is an algebraic number?

Published on 24 Mar 2026 - 19:14

score 105 · Answer 2 · 2026-03-25 05:09:03

105

Views

Changing digits of an irrational allowed?

Published on 25 Mar 2026 - 5:09

score 48 · Answer 3 · 2026-03-24 22:04:06

48

Views

Can a limit of form$\ \frac{0}{0}$ be rational if the numerator is the difference of transcendental functions, and the denominator a polynomial one?

Published on 24 Mar 2026 - 22:04

score 133 · Answer 4 · 2026-03-25 13:52:53

133

Views

Quotient of two rational sequences and the nature of its limit

Published on 25 Mar 2026 - 13:52

score 102 · Answer 5 · 2026-03-25 03:44:34

102

Views

As$\ n \to \infty$, can a transcendental function$\ f\left(1+ \frac{1}{n}\right)$ to the power of$\ n$ tend to a rational power of$\ e$?

Published on 25 Mar 2026 - 3:44

score 39 · Answer 6 · 2026-03-25 11:28:51

39

Views

Let$\ \lim_{n\to \infty} \frac{ \ln n}{f(n)}=1$. If$\ a,b,c$ are natural, can we have$\ a^{b+c \ln n}\sim a^{c f(n)}$?

Published on 25 Mar 2026 - 11:28

score 1.6k · Answer 7 · 2026-03-24 17:17:25

1.6k

Views

Is a trigonometric function applied to a rational multiple of $\pi$ always algebraic?

Published on 24 Mar 2026 - 17:17

score 1.6k · Answer 8 · 2026-03-25 13:16:15

1.6k

Views

For which $x$ is $e^x$ rational? Transcendental?

Published on 25 Mar 2026 - 13:16

score 270 · Answer 9 · 2026-03-25 14:29:18

270

Views

Why is Chaitin's constant absolutely normal?

Published on 25 Mar 2026 - 14:29

score 94 · Answer 10 · 2026-03-25 01:29:33

94

Views

Is there a direct proof that pi is not the root of an algebraic equation whose degree is a power of 2

Published on 25 Mar 2026 - 1:29

score 1.2k · Answer 11 · 2026-03-25 14:22:42

1.2k

Views

Is it known if $\pi + e$ is transcendental over the rational numbers?

Published on 25 Mar 2026 - 14:22

score 399 · Answer 12 · 2026-03-24 16:14:58

399

Views

Do we know if all simple extensions of the field of rational numbers by transcendental numbers are not equal?

Published on 24 Mar 2026 - 16:14

score 114 · Answer 13 · 2026-03-25 03:53:42

114

Views

Existence of a $\varphi \in \mathbb{R}$ such that $\cos(\varphi)$ is transcendental

Published on 25 Mar 2026 - 3:53

score 999 · Answer 14 · 2026-03-24 22:50:22

999

Views

What is the probability that a number chosen at random in $[0,1]$ is transcendental?

Published on 24 Mar 2026 - 22:50

score 588 · Answer 15 · 2026-03-25 17:53:12

588

Views

Why are numeric methods the only technique available to solving $\ln(x) = \sin(x)$? Is this $x$ transcendental?

Published on 25 Mar 2026 - 17:53

List Question

Does $6^x+3^x=10$ have an solution that is an algebraic number?

Changing digits of an irrational allowed?

Can a limit of form$\ \frac{0}{0}$ be rational if the numerator is the difference of transcendental functions, and the denominator a polynomial one?

Quotient of two rational sequences and the nature of its limit

As$\ n \to \infty$, can a transcendental function$\ f\left(1+ \frac{1}{n}\right)$ to the power of$\ n$ tend to a rational power of$\ e$?

Let$\ \lim_{n\to \infty} \frac{ \ln n}{f(n)}=1$. If$\ a,b,c$ are natural, can we have$\ a^{b+c \ln n}\sim a^{c f(n)}$?

Is a trigonometric function applied to a rational multiple of $\pi$ always algebraic?

For which $x$ is $e^x$ rational? Transcendental?

Why is Chaitin's constant absolutely normal?

Is there a direct proof that pi is not the root of an algebraic equation whose degree is a power of 2

Is it known if $\pi + e$ is transcendental over the rational numbers?

Do we know if all simple extensions of the field of rational numbers by transcendental numbers are not equal?

Existence of a $\varphi \in \mathbb{R}$ such that $\cos(\varphi)$ is transcendental

What is the probability that a number chosen at random in $[0,1]$ is transcendental?

Why are numeric methods the only technique available to solving $\ln(x) = \sin(x)$? Is this $x$ transcendental?

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