Question

Proof: Cubic Polynomial with Rational Coefficients and Roots

score 301 · Answer 1 · 2026-04-01 18:28:21

301

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Proof: Cubic Polynomial with Rational Coefficients and Roots

Published on 01 Apr 2026 - 18:28

score 92 · Answer 2 · 2021-04-21 07:27:21

92

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Does the Nested Harmonic Sequence Cover $(0,1] \cap \mathbb Q$?

Published on 21 Apr 2021 - 7:27

score 76 · Answer 3 · 2021-04-23 12:36:28

76

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Proving a Dedekind Cut for Rational Numbers

Published on 23 Apr 2021 - 12:36

score 86 · Answer 4 · 2021-04-26 17:34:35

86

Views

Determine the largest and smallest of the rational numbers $x$, $y$, $z$ if $x^2+4y^2+z^2-4xy-4yz+2xz-2x+2z+2=0$

Published on 26 Apr 2021 - 17:34

score 563 · Answer 5 · 2021-05-02 09:19:32

563

Views

Prove that $\sqrt[3]{45+29\sqrt{2}} +\sqrt[3]{45-29\sqrt{2}} $ is rational.

Published on 02 May 2021 - 9:19

score 85 · Answer 6 · 2026-04-08 11:10:32

85

Views

Does there exist a positive integer $n$ such that $P^n = I$, where $P$ is a rotation matrix?

Published on 08 Apr 2026 - 11:10

score 82 · Answer 7 · 2026-03-31 19:44:49

82

Views

The probability of recovering from a disease

Published on 31 Mar 2026 - 19:44

score 47 · Answer 8 · 2021-05-05 11:56:27

47

Views

Value for a variable as a rational number

Published on 05 May 2021 - 11:56

score 238 · Answer 9 · 2026-03-26 09:41:05

238

Views

Examples of rational numbers with large denominators appearing unexpectedly.

Published on 26 Mar 2026 - 9:41

score 884 · Answer 10 · 2026-04-08 11:02:55

884

Views

Proving that $\sqrt{13+\sqrt{52}} - \sqrt{13}$ is irrational.

Published on 08 Apr 2026 - 11:02

score 425 · Answer 11 · 2021-05-17 07:21:25

425

Views

How can I prove that set T is countably infinite? Countable and uncountable sets; rational numbers

Published on 17 May 2021 - 7:21

score 58 · Answer 12 · 2021-05-19 15:34:53

58

Views

If $a$ is a positive integer and $p$ is prime, then $\log_{p}(a)$ is rational if and only if $a$ is a power of $p$.

Published on 19 May 2021 - 15:34

score 103 · Answer 13 · 2021-05-20 17:27:55

103

Views

Find all $\alpha$ such that $\frac{\cos \alpha - a \sin \alpha}{a \cos \alpha + \sin \alpha}$ is rational (given $a$ rational)

Published on 20 May 2021 - 17:27

score 63 · Answer 14 · 2021-05-22 10:48:04

63

Views

Why $\mathbb{Q}(\sqrt{\alpha})\neq \mathbb{Q}(\sqrt{\beta})$ if $\sqrt{\alpha \beta} \notin \mathbb{Q}$?

Published on 22 May 2021 - 10:48

score 99 · Answer 15 · 2026-03-27 00:05:05

99

Views

Two properties of the set of Bernoulli numbers

Published on 27 Mar 2026 - 0:05

List Question

Proof: Cubic Polynomial with Rational Coefficients and Roots

Does the Nested Harmonic Sequence Cover $(0,1] \cap \mathbb Q$?

Proving a Dedekind Cut for Rational Numbers

Determine the largest and smallest of the rational numbers $x$, $y$, $z$ if $x^2+4y^2+z^2-4xy-4yz+2xz-2x+2z+2=0$

Prove that $\sqrt[3]{45+29\sqrt{2}} +\sqrt[3]{45-29\sqrt{2}} $ is rational.

Does there exist a positive integer $n$ such that $P^n = I$, where $P$ is a rotation matrix?

The probability of recovering from a disease

Value for a variable as a rational number

Examples of rational numbers with large denominators appearing unexpectedly.

Proving that $\sqrt{13+\sqrt{52}} - \sqrt{13}$ is irrational.

How can I prove that set T is countably infinite? Countable and uncountable sets; rational numbers

If $a$ is a positive integer and $p$ is prime, then $\log_{p}(a)$ is rational if and only if $a$ is a power of $p$.

Find all $\alpha$ such that $\frac{\cos \alpha - a \sin \alpha}{a \cos \alpha + \sin \alpha}$ is rational (given $a$ rational)

Why $\mathbb{Q}(\sqrt{\alpha})\neq \mathbb{Q}(\sqrt{\beta})$ if $\sqrt{\alpha \beta} \notin \mathbb{Q}$?

Two properties of the set of Bernoulli numbers

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