List questions from rationality-testing

Published on 13 Apr 2026 - 21:26

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Rational or irrational sum and the integral

Published on 13 Apr 2026 - 4:25

281

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Show that $\lim_{k\to\infty}\lim_{j\to\infty}\cos^{2j}k!\pi x=0$

Published on 14 Apr 2026 - 16:56

105

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Is it possible to cut the unit square in triangles of the same area such that one of the vertices has irrational coordinates?

Published on 17 Apr 2026 - 6:56

496

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Square roots proved irrational by denominator descent

Published on 14 Apr 2026 - 15:05

783

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Is there a way to prove numbers irrational in general?

Published on 11 Apr 2026 - 22:38

51

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Shifting roots in infinite sums of polynomials

Published on 10 Apr 2026 - 21:43

1.6k

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Is it rational or irrational?

Published on 13 Apr 2026 - 4:14

931

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Rational with finite decimals values for sine, cosine, and tangent

Published on 15 Apr 2026 - 21:26

94

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Does $x^3 - \frac{m}{n}\sqrt{5}x - 1$ has rational root?

Published on 15 Apr 2026 - 0:12

93

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Prove that $\sqrt[3]p+\sqrt[3]{p^5}$ is irrational if $p$ is prime

Published on 15 Apr 2026 - 11:42

145

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What is the reasoning behind $y=\frac{x(x^2+3D)}{ 3x^{2}+D }$ in Dedekind's "Essays On The Theory Of Numbers"?

Published on 14 Apr 2026 - 14:54

15.7k

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Value of cos 1 (angle is in radians)?

Published on 10 Apr 2026 - 18:49

43

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If $\sum_{i=0}^\infty p_1^{i}p_2^{-a_i}$ converges and is rational does that imply that $\sum_{i=0}^\infty p_2^{-a_i}$ is also rational

Published on 15 Apr 2026 - 22:00

36

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Is a definite integral of $f(x)$ rational if $f(x)$ is rational at the endpoints and f(0)=0?

Published on 16 Apr 2026 - 12:04

List Question

Proof that $\sqrt[3]{17}$ is irrational

Rational or irrational sum and the integral

Show that $\lim_{k\to\infty}\lim_{j\to\infty}\cos^{2j}k!\pi x=0$

Is it possible to cut the unit square in triangles of the same area such that one of the vertices has irrational coordinates?

Square roots proved irrational by denominator descent

Is there a way to prove numbers irrational in general?

Shifting roots in infinite sums of polynomials

Is it rational or irrational?

Rational with finite decimals values for sine, cosine, and tangent

Does $x^3 - \frac{m}{n}\sqrt{5}x - 1$ has rational root?

Prove that $\sqrt[3]p+\sqrt[3]{p^5}$ is irrational if $p$ is prime

What is the reasoning behind $y=\frac{x(x^2+3D)}{ 3x^{2}+D }$ in Dedekind's "Essays On The Theory Of Numbers"?

Value of cos 1 (angle is in radians)?

If $\sum_{i=0}^\infty p_1^{i}p_2^{-a_i}$ converges and is rational does that imply that $\sum_{i=0}^\infty p_2^{-a_i}$ is also rational

Is a definite integral of $f(x)$ rational if $f(x)$ is rational at the endpoints and f(0)=0?

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