Grigory M
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# 2,689 Actions

 Jan18 reviewed Close (Soft Question) How active an area of research is Non-Commutative Geometry? Jan18 reviewed Close How many pairs of integers $(A, B)$ are there in the range $[1,\ldots, N]$, such that $\gcd(A,B) = B$? Jan18 comment Does there exist $\mathbf{Q} \subset R \subset \mathbf{C}$, $R$ ring & not field There is an injective map from $\mathbb Q[x]\to\mathbb R$ taking $x$ to $\pi$. Call the image of this map whatever you like — but that's an example. Jan17 revised Calculate all the generators in $\mathbb{Z}/61$ edited tags Jan17 comment Showing ${n + a - 1 \choose a - 1} = \sum_{k = 0}^{\left\lfloor n/2 \right\rfloor} {a \choose n-2k}{k+a-1 \choose a-1}$ Jan17 comment Elementary proof of the fact that any orientable 3-manifold is parallelizable «The second surprise in this story» — that's, IMHO, the most interesting part... Jan17 comment Closed-form solution for $f(n) = \sum_{k>0}\binom{n}{2k}x^{k}$ without $\sqrt{x}$ @1234 $\frac{P(x)+P(-x)}2$ extracts even terms from any polynomial $P$, you know... Jan17 comment Closed-form solution for $f(n) = \sum_{k>0}\binom{n}{2k}x^{k}$ without $\sqrt{x}$ Well, do you know the answer for just $\sum \binom nlx^l$? Jan17 comment Elementary proof of the fact that any orientable 3-manifold is parallelizable Do you know the standard proof («$w_1=w_2=0$ implies parallelizable by elementary obstruction theory» + «$w_1=0$ implies $w_2=0$ by Wu's formulas»)? It's not that hard — and at least the first part is, in a sense, the most straightforward approach possible (but I indeed don't know any intuitive explanation of the second part). Jan16 reviewed Leave Closed $\mathcal A$ is empty, what is $\bigcap_{S\in\mathcal A}S$? Jan16 comment If $a,b,c$ are real numbers all less than or equal to $1$ such that $a+b+c=0$ , then is it true that $(1-a)(1-b)(1-c) \le 1$? «which is true» — why, actually? ($ab$ can be negative) Jan16 comment On ${-1 \choose 0}=1$, can I assume that $\frac{(-1)!}{(-1)!}=1$? OK, I apologise — this question was not completely clear as written — but it's a) not a duplicate of the linked question; b) can be reasonably answered. Jan16 comment On ${-1 \choose 0}=1$, can I assume that $\frac{(-1)!}{(-1)!}=1$? Jan16 reviewed Looks OK Showing that the roots of a polynomial with descending positive coefficients lie in the unit disc. Jan16 reviewed Leave Open Intersecting Circumcircles Jan16 reviewed Leave Closed Finding the closed form for $\sum_{n=1}^{\infty }\frac{\zeta (4n)}{\beta^{4n-1}}$ Jan16 reviewed Looks OK constant-curvature Riemannian metric for Bring's surface Jan16 reviewed Looks OK Proof that $f:\mathbb R\to[-1,1], f(x)=\cos x$ is surjective Jan16 reviewed No Action Needed The convergence of $\sum_{n=2}^{+\infty} \frac{1}{\sqrt{n}} \ln(\frac{n+1}{n-1})$ Jan16 reviewed No Action Needed conjugation of Lie groups and homotopy group