List questions from algebraic-numbers

Published on 04 Dec 2023 - 1:31

285

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Is there an elementary proof that $2^{\sqrt{2}}$ is irrational?

Published on 22 Jan 2024 - 3:54

195

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Can $x\sin(x)$ be algebraic when it is not $0$?

Published on 13 Feb 2024 - 0:44

3.9k

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Prove: if $a$ and $b$ are algebraic, then $a + b$, $a - b$ and ab are also algebraic

Published on 16 Apr 2015 - 13:12

2.7k

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Algebraic numbers as roots of polynomials of degree $n$ are countable.

Published on 08 Jul 2015 - 20:02

1.8k

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Is there a general formula for $\sin( {p \over q} \pi)$?

Published on 21 Nov 2015 - 16:34

4.5k

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What if $\pi$ was an algebraic number? (significance of algebraic numbers)

Published on 16 Aug 2013 - 0:28

74.5k

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Prove that the set of all algebraic numbers is countable

Published on 10 Sep 2013 - 5:51

4.2k

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Prove that the set of all algebraic numbers is countable: proof using fundamental theorem of algebra

Published on 21 Jul 2017 - 14:51

172

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Classes of transcendental numbers?

Published on 10 Aug 2017 - 14:52

146

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Theorem 13, Chapter II of Marcus' Number Fields

Published on 30 Aug 2017 - 13:05

63

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Proof verification on countability of algebraic numbers?

Published on 21 Sep 2017 - 17:29

226

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Is it possible to express $\sqrt[6]{2}$ as rational combination of $1, \sqrt{2}, \sqrt[4]{2}$?

Published on 29 Oct 2017 - 16:29

152

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Finding a polynomial that proves $\sqrt6$ is an algebraic number

Published on 14 Nov 2017 - 6:53

587

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Finding minimal polynomial over $\mathbb{Q}$

Published on 14 Nov 2017 - 8:28

List Question

Show that $\pi$ is not algebraic over the field $\mathbb A$ of algebraic numbers.

Is there an elementary proof that $2^{\sqrt{2}}$ is irrational?

Can $x\sin(x)$ be algebraic when it is not $0$?

Prove: if $a$ and $b$ are algebraic, then $a + b$, $a - b$ and ab are also algebraic

Algebraic numbers as roots of polynomials of degree $n$ are countable.

Is there a general formula for $\sin( {p \over q} \pi)$?

What if $\pi$ was an algebraic number? (significance of algebraic numbers)

Prove that the set of all algebraic numbers is countable

Prove that the set of all algebraic numbers is countable: proof using fundamental theorem of algebra

Classes of transcendental numbers?

Theorem 13, Chapter II of Marcus' Number Fields

Proof verification on countability of algebraic numbers?

Is it possible to express $\sqrt[6]{2}$ as rational combination of $1, \sqrt{2}, \sqrt[4]{2}$?

Finding a polynomial that proves $\sqrt6$ is an algebraic number

Finding minimal polynomial over $\mathbb{Q}$

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