Question

What is the solution of $\frac{x^3}{y^3+z^3}+\frac{y^3}{x^3+z^3}+\frac{z^3}{y^3+x^3}=1$ in rational?

score 235 · Answer 1 · 2026-04-15 20:35:50

235

Views

What is the solution of $\frac{x^3}{y^3+z^3}+\frac{y^3}{x^3+z^3}+\frac{z^3}{y^3+x^3}=1$ in rational?

Published on 15 Apr 2026 - 20:35

score 1k · Answer 2 · 2026-04-14 04:10:44

1k

Views

Multiplication of two irrational to give rational

Published on 14 Apr 2026 - 4:10

score 282 · Answer 3 · 2026-04-13 16:42:22

282

Views

"If $a+a^3$ is irrational, then $a+a^2$ is also irrational".

Published on 13 Apr 2026 - 16:42

score 361 · Answer 4 · 2026-04-12 01:42:49

361

Views

If $r\in\mathbb{Q}\setminus\mathbb{Z}$ is it possible that $r^{r^{r^r}}\in \mathbb{Q}$?

Published on 12 Apr 2026 - 1:42

score 59 · Answer 5 · 2026-04-12 11:41:01

59

Views

A question about the supremum of a rational set

Published on 12 Apr 2026 - 11:41

score 25 · Answer 6 · 2026-04-08 08:12:34

25

Views

Is Inducing Limits in Irrationality proof valid?

Published on 08 Apr 2026 - 8:12

score 74 · Answer 7 · 2026-04-13 09:53:01

74

Views

Is there an example of $\mathbb{R} \to \mathbb{R}$ function that produces only rationally independent numbers?

Published on 13 Apr 2026 - 9:53

score 175 · Answer 8 · 2026-04-11 19:17:37

175

Views

Proving the density of a function in an interval.

Published on 11 Apr 2026 - 19:17

score 65 · Answer 9 · 2026-04-09 06:18:04

65

Views

Are some irrational questions more irrational than others? (A-Level EPQ)

Published on 09 Apr 2026 - 6:18

score 112 · Answer 10 · 2026-04-14 06:04:34

112

Views

Square root of prime is irrational. Is this a valid proof?

Published on 14 Apr 2026 - 6:04

score 661 · Answer 11 · 2026-04-09 04:18:40

661

Views

Is it possible to convert an irrational number into rational by using a different number system?

Published on 09 Apr 2026 - 4:18

score 70 · Answer 12 · 2026-04-16 11:04:35

70

Views

Proving $\sin\left(\frac{2\pi}{p}\right)$ is irrational where $p\geqslant3$ is prime

Published on 16 Apr 2026 - 11:04

score 53 · Answer 13 · 2026-04-17 09:55:37

53

Views

Rationality of $\log_b a$ when at least $a$ or $b$ is irrational and $a,b>1$

Published on 17 Apr 2026 - 9:55

score 245 · Answer 14 · 2026-04-11 03:37:52

245

Views

Polynomial with natural coefficients at irrational points

Published on 11 Apr 2026 - 3:37

score 164 · Answer 15 · 2026-04-13 15:05:53

164

Views

Proving $\pi$ is irrational without arguing by contradiction

Published on 13 Apr 2026 - 15:05

List Question

What is the solution of $\frac{x^3}{y^3+z^3}+\frac{y^3}{x^3+z^3}+\frac{z^3}{y^3+x^3}=1$ in rational?

Multiplication of two irrational to give rational

"If $a+a^3$ is irrational, then $a+a^2$ is also irrational".

If $r\in\mathbb{Q}\setminus\mathbb{Z}$ is it possible that $r^{r^{r^r}}\in \mathbb{Q}$?

A question about the supremum of a rational set

Is Inducing Limits in Irrationality proof valid?

Is there an example of $\mathbb{R} \to \mathbb{R}$ function that produces only rationally independent numbers?

Proving the density of a function in an interval.

Are some irrational questions more irrational than others? (A-Level EPQ)

Square root of prime is irrational. Is this a valid proof?

Is it possible to convert an irrational number into rational by using a different number system?

Proving $\sin\left(\frac{2\pi}{p}\right)$ is irrational where $p\geqslant3$ is prime

Rationality of $\log_b a$ when at least $a$ or $b$ is irrational and $a,b>1$

Polynomial with natural coefficients at irrational points

Proving $\pi$ is irrational without arguing by contradiction

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