# Tagged Questions

For questions concerning a specific proof, asking for verification, identifying errors, suggestions for improvement, etc.

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### Let $a,b,m,n\in\mathbb{N^*}$ with $\gcd(a,b)=1$. Is my proof correct that $(a^m,b^n)=1$?

$\gcd(a,b)=1 \iff \exists k,l \in \mathbb{N^*}(ka+lb=1)$, by Bezout's identity. Suppose $k=a^{m-1}\in \mathbb{N}$ and $l=b^{n-1}\in \mathbb{N}$. Then $ka+lb=a^{m-1}a+b^{n-1}b=a^m+b^n=1$, as ...
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### Prove that $R\cap S$ is symmetric, transitive, and anti-symmetric.

If you can confirm these are done correctly or offer another way to do so I would greatly appreciate it. Also how would you go about proving $R\cap S$ is reflexive? What assumption if any would be ...
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### Proof that linear difference operator, $(Ļ-1)^{k+1} (p) = 0$ for all $p$ $\epsilon$ $\mathbb{Q}[t]$, with $deg(p) \leq k$.

I am trying to prove that linear difference operator, $(Ļ-1)^{k+1} (p) = 0$ for all $p$ $\epsilon$ $\mathbb{Q}[t]$, with $deg(p) \leq k$. In this case $\sigma(t)=t+1$ and $\sigma($anything else$)=$...
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### Does this family of sequences have the limit $\left(\frac{x^{2p}-y^{2p}}{2p(\ln x-\ln y)} \right)^{1/2p}$ for $p \in \mathbb{R}$?

Define the following family of one parameter sequences: $$a_0=x,~~~b_0=y$$ $$a_{n+1}=\sqrt{a_n \sqrt[p]{\frac{a_n^p+b_n^p}{2}}},~~~b_{n+1}=\sqrt{b_n \sqrt[p]{\frac{a_n^p+b_n^p}{2}}}$$ I conjecture ...
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### Proving that $-\Delta+V$ on some domain is self-adjoint

This question may look as a "proof-reading" question, but what I ask is if I correctly understand the way these concepts work, by showing how I think about them. Suppose I have the following three ...
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### Prove $\lim\frac{4\sin(n^2)}{3n}=0$
Prove $\lim\frac{4\sin(n^2)}{3n}=0$ Using the fact that $\left|s_n-s\right|\lt \epsilon$ I'm finding it difficult to solve for $n$. I recognize the function is bounded between $-1$ and $1$, but I ...