# All Questions

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### Normal polytopes - counterexample?

An integral polytope $P$ is normal if all lattice points inside the integer dilation $kP$ can be expressed as $p_1+p_2+\dots+p_k$, where $p_i \in P$ are lattice points. I am looking for an example ...
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### Divisibility by Euler's Totient Function

Let $n$ be an odd composite number $(>1)$ and $p$ be an odd prime such that: $p\nmid n$, $\phi(n)\nmid (n-1)$, For some even part of $\phi(n)$ (say, $\phi(n_0)$), $\phi(n_0)\nmid (n-1)$, ...
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### A question about uncountable subsets [on hold]

Let X={A belongs to N: A and N\A are infinite}. Prove that X is uncountable. This question bothers me all night. Can any one solve it from the angle of P(N)\X ? Sorry I dont know the rules here. I ...
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### What set theoretical questions could never be answered by Turing machines of arbitrary cardinality?

Let us assume that there are Turing machines of arbitrary cardinality, by that I mean they can have input tapes of any arbitrarily high cardinality and compute for a number of steps also of ...
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### Sharpening a bound on $\zeta'(s)$

I want to find an upper bound for $\zeta'(s)$ along a vertical line $\Re(s)=b$, where $-1<b<0$. One way to do this is using $$\frac{\zeta'(b+iT)}{\zeta(b+iT)}=O_b(\log T)$$ and ...
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### “Paradoxes” in $\mathbb{R}^n$

One may think of this question as a duplicate of this one. I see it more like an extension. The "inscribed sphere paradox" discussed in the aforementioned question states that if you inscribe a ...
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### real algebraic geometry software?

Does anyone have suggestions/experience for any software packages to study real algebraic varieties (for example, counting connected components of hypersurfaces, figuring out the topological type of ...
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### Graph Theory is the slum of Topology (?) [on hold]

(Edited in accordance with suggestions in comments.) I remember once I read a quote that sounded like "graph theory is the slum of topology" (please approximate). I can not find it on the web, and I ...
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### Homotopy with non piece-wise linear boundary

in the middle of a long proof I encounter the following problem. Let $E$ be a closed and convex set in $\mathbb R^n$ such that for all $\vec x\in E$ it holds that $\sum_ix_i=1$. (We can understand ...
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### Is Laplacian matrix singular? [on hold]

I'd like to ask is Laplacian L matrix singular? Than if it is singular, how it is possible do inverse and lu factor of Laplacian?
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### the Action of $SL_2(\mathbb{R})$ on a fundamental domain of $\Gamma$
Let $F=\{z\in H: |z|\geq1, |Re(z)|\leq 1/2\}$. It is a fundamental domain of the modular group $\Gamma$ acting on the upper half plane $H$. (Strictly speaking, one should take part of the boundary ...