Question

What is the smallest integer $N>2$, such that $x^5+y^5 = N$ has a rational solution?

score 203 · Answer 1 · 2026-03-21 16:50:50

203

Views

What is the smallest integer $N>2$, such that $x^5+y^5 = N$ has a rational solution?

Published on 21 Mar 2026 - 16:50

score 74 · Answer 2 · 2026-03-24 19:30:30

74

Views

I don't understand why my college algebra book is picking when to multiply factors

Published on 24 Mar 2026 - 19:30

score 470 · Answer 3 · 2026-03-22 16:09:49

470

Views

Non-galois real extensions of $\mathbb Q$

Published on 22 Mar 2026 - 16:09

score 188 · Answer 4 · 2026-03-24 11:42:36

188

Views

A variation of the argument to prove that $\{m/n:n \text{ is odd },n,m \in \mathbb{Z}\}$ is a PID

Published on 24 Mar 2026 - 11:42

score 314 · Answer 5 · 2026-03-20 15:17:06

314

Views

Almost have a group law: $(x,y)*(a,b) = (xa + yb, xb + ya)$ with rational components.

Published on 20 Mar 2026 - 15:17

score 89 · Answer 6 · 2026-03-22 13:18:30

89

Views

When are $\alpha$ and $\cos\alpha$ both rational?

Published on 22 Mar 2026 - 13:18

score 496 · Answer 7 · 2026-03-22 19:49:41

496

Views

What is the decimal form of 1/299,792,458

Published on 22 Mar 2026 - 19:49

score 1.1k · Answer 8 · 2026-03-20 08:30:50

1.1k

Views

Proving that the sequence $\{\frac{3n+5}{2n+6}\}$ is Cauchy.

Published on 20 Mar 2026 - 8:30

score 5.4k · Answer 9 · 2026-03-22 04:09:14

5.4k

Views

Is this a valid proof? If $a$ and $b$ are rational, $a^b$ is rational.

Published on 22 Mar 2026 - 4:09

score 247 · Answer 10 · 2026-03-22 10:46:30

247

Views

What is the identity element for the subgroup $H=\{a+b\sqrt{2}:a,b\in\mathbb{Q},\text{$a$ and $b$ are not both zero}\}$ of the group $\mathbb{R}^*$?

Published on 22 Mar 2026 - 10:46

score 111 · Answer 11 · 2026-03-23 14:18:12

111

Views

Among $2n-1$ irrationals there are $x_1,\dots,x_n$ such that for rationals $a_i\ge0$ with $\sum_{i=1}^{n}a_i>0$, $\sum_{i=1}^{n}a_ix_i$ is irrational

Published on 23 Mar 2026 - 14:18

score 3.9k · Answer 12 · 2026-03-24 19:08:59

3.9k

Views

Proof that there is no rational solutions to the equation $x^3+2x-1=0$

Published on 24 Mar 2026 - 19:08

score 103 · Answer 13 · 2026-03-17 13:01:15

103

Views

Linear transformation from irrationals to rationals with a constraint

Published on 17 Mar 2026 - 13:01

score 14.1k · Answer 14 · 2026-03-17 10:46:27

14.1k

Views

What is the algebraic closure of $\mathbb{Q}$?

Published on 17 Mar 2026 - 10:46

score 84 · Answer 15 · 2026-03-17 04:18:41

84

Views

Rationalizing an expression; when to stop, what is the higher level purpose?

Published on 17 Mar 2026 - 4:18

List Question

What is the smallest integer $N>2$, such that $x^5+y^5 = N$ has a rational solution?

I don't understand why my college algebra book is picking when to multiply factors

Non-galois real extensions of $\mathbb Q$

A variation of the argument to prove that $\{m/n:n \text{ is odd },n,m \in \mathbb{Z}\}$ is a PID

Almost have a group law: $(x,y)*(a,b) = (xa + yb, xb + ya)$ with rational components.

When are $\alpha$ and $\cos\alpha$ both rational?

What is the decimal form of 1/299,792,458

Proving that the sequence $\{\frac{3n+5}{2n+6}\}$ is Cauchy.

Is this a valid proof? If $a$ and $b$ are rational, $a^b$ is rational.

What is the identity element for the subgroup $H=\{a+b\sqrt{2}:a,b\in\mathbb{Q},\text{$a$ and $b$ are not both zero}\}$ of the group $\mathbb{R}^*$?

Among $2n-1$ irrationals there are $x_1,\dots,x_n$ such that for rationals $a_i\ge0$ with $\sum_{i=1}^{n}a_i>0$, $\sum_{i=1}^{n}a_ix_i$ is irrational

Proof that there is no rational solutions to the equation $x^3+2x-1=0$

Linear transformation from irrationals to rationals with a constraint

What is the algebraic closure of $\mathbb{Q}$?

Rationalizing an expression; when to stop, what is the higher level purpose?

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