List questions from rational-numbers

Published on 28 Mar 2026 - 6:24

187

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Prove $X^4-5X^3+3X-2$ is irreducible over the rationals.

Published on 03 Apr 2026 - 11:48

63

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Existence of open interval $(x − δ_k, x + δ_k)$ which does not contain any rational number with denominator $k.$

Published on 26 Mar 2026 - 9:27

50

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Prove that rational coefficients $\implies$ rational root

Published on 07 May 2023 - 15:47

56

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If $\operatorname{Im}(z) \in\Bbb Q$ for $|z|=1$ then what about real and imaginary parts of $z^{2^n}$

Published on 16 May 2023 - 21:34

75

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Proving there are no rational cubic roots between two $f^3$ and $(f+1)^3$

Published on 02 Apr 2026 - 10:34

57

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Can a logarithm be written as a power using only rational numbers?

Published on 02 Apr 2026 - 10:41

67

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$\mathbb Q$ is the only infinite prime field

Published on 21 May 2023 - 14:27

57

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Educated guess for algebraic approximation formula.

Published on 30 Mar 2026 - 8:11

60

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Representation of non zero rational number

Published on 29 May 2023 - 13:12

46

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Is given statement indeed true?

Published on 01 Apr 2026 - 20:56

60

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Relation between $\mathbb{Q}$ and $\mathbb{Z}^2$

Published on 21 Mar 2026 - 20:25

79

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Proof: Let $x$, $y \in Q$, $y > 0$, $x > 1$. Then there is an integer $n$ such that $x^n < y ≤ x^{n+1}$.

Published on 06 Jun 2023 - 16:54

58

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Rudin's PMA, Chapter 1 Appendix Proof of Theorem 1.19 Step 6 - Proof of (M4)

Published on 06 Jun 2023 - 19:54

82

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what does it mean for a rational number to be "complicated"?

Published on 02 Apr 2026 - 3:46

List Question

Rational solutions for $x^3+y^3=1$ where both x and y are non-negative

Prove $X^4-5X^3+3X-2$ is irreducible over the rationals.

Existence of open interval $(x − δ_k, x + δ_k)$ which does not contain any rational number with denominator $k.$

Prove that rational coefficients $\implies$ rational root

If $\operatorname{Im}(z) \in\Bbb Q$ for $|z|=1$ then what about real and imaginary parts of $z^{2^n}$

Proving there are no rational cubic roots between two $f^3$ and $(f+1)^3$

Can a logarithm be written as a power using only rational numbers?

$\mathbb Q$ is the only infinite prime field

Educated guess for algebraic approximation formula.

Representation of non zero rational number

Is given statement indeed true?

Relation between $\mathbb{Q}$ and $\mathbb{Z}^2$

Proof: Let $x$, $y \in Q$, $y > 0$, $x > 1$. Then there is an integer $n$ such that $x^n < y ≤ x^{n+1}$.

Rudin's PMA, Chapter 1 Appendix Proof of Theorem 1.19 Step 6 - Proof of (M4)

what does it mean for a rational number to be "complicated"?

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