Question

Proving Irreducibility of $X^{2p}+pX^n-1$ in $\mathbb{Z}[X]$

score 204 · Answer 1 · 2026-04-14 20:33:12

204

Views

Proving Irreducibility of $X^{2p}+pX^n-1$ in $\mathbb{Z}[X]$

Published on 14 Apr 2026 - 20:33

score 162 · Answer 2 · 2026-04-11 18:59:51

162

Views

Is a finite union of countable sets at most countable?

Published on 11 Apr 2026 - 18:59

score 119 · Answer 3 · 2026-04-17 07:17:38

119

Views

If $D_1,D_2 \in \mathbb R ^2, D_1 \cap D_2 \neq \emptyset $ are two open discs, then $\exists D_{(a,b)} \subset D_1 \cap D_2$

Published on 17 Apr 2026 - 7:17

score 258 · Answer 4 · 2026-04-16 17:21:58

258

Views

Family of Generalized Integrals ${I}(a,b,p)=\int_0^{ab} \left( \left\{\frac{x}{a}\right\}-p\right) \left( \left\{\frac{x}{b}\right\}-p\right) \; dx$

Published on 16 Apr 2026 - 17:21

score 85 · Answer 5 · 2026-04-09 10:49:10

85

Views

Proof verification of a number theory problem involving sequences.

Published on 09 Apr 2026 - 10:49

score 712 · Answer 6 · 2026-04-15 02:33:32

712

Views

Find the value of $\sin^{-1}(\cos 2)-\cos^{-1}(\sin 2) +\tan^{-1}(\cot 4) -\cot^{-1}(\tan 4)+\sec^{-1}(\csc 6)-\csc^{-1}(\sec 6)$

Published on 15 Apr 2026 - 2:33

score 72 · Answer 7 · 2026-04-10 11:57:56

72

Views

A kind of Cauchy's Condensation Test?

Published on 10 Apr 2026 - 11:57

score 45 · Answer 8 · 2026-04-14 11:09:34

45

Views

Is there any error in my proof of '$\lim_{x\to\infty} ((\frac{x}{x+k})^x)=\frac{1}{e^k}$'

Published on 14 Apr 2026 - 11:09

score 280 · Answer 9 · 2026-04-13 21:47:53

280

Views

Let $f$ be continuous. If $f(x) = 0 \implies f$ is strictly increasing at $x$, then $f$ has at most one root.

Published on 13 Apr 2026 - 21:47

score 756 · Answer 10 · 2026-04-12 06:29:36

756

Views

The flow of Killing vector field is an isometry-proof verification

Published on 12 Apr 2026 - 6:29

score 28 · Answer 11 · 2026-04-15 18:40:12

28

Views

Occupancy rate for a row of houses

Published on 15 Apr 2026 - 18:40

score 155 · Answer 12 · 2026-04-15 13:50:57

155

Views

Is this proof valid to prove that $F(x)-G(x)$ is always non zero?

Published on 15 Apr 2026 - 13:50

score 48 · Answer 13 · 2026-03-25 04:43:57

48

Views

Find the form of the quadratic approximation of a function $f$ at a certain point $a$ and find its euclidean normal form

Published on 25 Mar 2026 - 4:43

score 54 · Answer 14 · 2026-04-14 22:47:05

54

Views

Prove: if for all $x,y \in A \subset \Bbb R$, $|x-y|<1$, then $\sup A-\inf A \le 1$

Published on 14 Apr 2026 - 22:47

score 60 · Answer 15 · 2026-04-16 13:09:07

60

Views

If $x$ takes a negative value, prove that $\sin^{-1}x=-\cos^{-1}\sqrt{1-x^2}$

Published on 16 Apr 2026 - 13:09

List Question

Proving Irreducibility of $X^{2p}+pX^n-1$ in $\mathbb{Z}[X]$

Is a finite union of countable sets at most countable?

If $D_1,D_2 \in \mathbb R ^2, D_1 \cap D_2 \neq \emptyset $ are two open discs, then $\exists D_{(a,b)} \subset D_1 \cap D_2$

Family of Generalized Integrals ${I}(a,b,p)=\int_0^{ab} \left( \left\{\frac{x}{a}\right\}-p\right) \left( \left\{\frac{x}{b}\right\}-p\right) \; dx$

Proof verification of a number theory problem involving sequences.

Find the value of $\sin^{-1}(\cos 2)-\cos^{-1}(\sin 2) +\tan^{-1}(\cot 4) -\cot^{-1}(\tan 4)+\sec^{-1}(\csc 6)-\csc^{-1}(\sec 6)$

A kind of Cauchy's Condensation Test?

Is there any error in my proof of '$\lim_{x\to\infty} ((\frac{x}{x+k})^x)=\frac{1}{e^k}$'

Let $f$ be continuous. If $f(x) = 0 \implies f$ is strictly increasing at $x$, then $f$ has at most one root.

The flow of Killing vector field is an isometry-proof verification

Occupancy rate for a row of houses

Is this proof valid to prove that $F(x)-G(x)$ is always non zero?

Find the form of the quadratic approximation of a function $f$ at a certain point $a$ and find its euclidean normal form

Prove: if for all $x,y \in A \subset \Bbb R$, $|x-y|<1$, then $\sup A-\inf A \le 1$

If $x$ takes a negative value, prove that $\sin^{-1}x=-\cos^{-1}\sqrt{1-x^2}$

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