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umagon at google mail


Jun
10
comment Proving an integer is non-negative by showing there is a vector space with it as its dimension.
The question is about 'Proving an integer is non-negative by showing there is a vector space with it as its dimension'. All quantities in RR are manifestly non-negative integers, aren't they?..
Jun
8
comment diophantine equation $ |x^2-py^2|=\frac{p-1}{2} $
AFAICS this answer is about Pell-type equations $ax^2-qy^2=f$ s.t. either $f/(a-q)$ or $f/a$ is a square. I don't see how this helps to answer the question.
Jun
6
comment A correspondence between generators of $H_n(\mathbb{R}^n,\mathbb{R}^n-\{0\})$ and eq. classes of orthonormal frames
Related: equivalent definitions of orientation
Jun
6
comment Prove that for $n$ and $m$ integers: $ 3^mn \mid \sum\limits_{k=0}^{m} {\binom{3m}{3k}}(3n-1)^k$
I wonder if RHS has a nice combinatorial interpretation...
Jun
2
comment Is it possible to get a formula for this summation
Try some small $n$'s. Do you have a conjecture about the answer?
May
31
comment Compute $\pi^n(S^1\times S^{n+1})$.
@Najib How so? (Are you confusing $\pi^n$ with $\pi_n$?)
May
31
comment Quadratic residue modulo $p$ iff quadratic residue module $p^k$
In other words: if $x^2=a\pmod{p^k}$ one can find $y$ s.t. $(x+p^ky)^2=a\pmod{p^{k+1}}$ (it's actually very easy since $(x+p^ky)^2=x^2+2p^ky\pmod{p^{k+1}}$).
May
31
comment Proving continuity by epsilon-delta proof for a function of two variables.
(Of course, once you know that composition of cont. functions is cont. and sum of cont. functions is continuous...)
May
30
comment Can you compute relative homology using simplicial chain complex?
Sure — if you know (or believe in) the result for absolute homology, just apply 5-lemma to the long exact sequence for the pair $(M,\partial M)$.
May
30
comment Logic behind cubic resolution of $x^4+px^2+qx+r=0$
...Maybe Dummit & Foote, ch. 14 (see esp. sec. 6–7) is not a bad reference (but I hope someone will give a better reference)
May
30
comment Logic behind cubic resolution of $x^4+px^2+qx+r=0$
Yes, there is some logic behind it — it is explained by Galois theory...
May
29
comment Elementary proof that $Gl_n(\mathbb R)$ and $Gl_m(R)$ are homeomorphic iff $n=m$
related (essentially duplicate of?): Elementary proof that $\mathbb{R}^n$ is not homeomorphic to $\mathbb{R}^m$
May
29
comment Why is $\sum\limits_{k=0}^{n}(-1)^k\binom{n}{k}^2=(-1)^{n/2}\binom{n}{n/2}$ if $n$ is even?
I don't see how Hagen von Eitzen's answer is any different from the first of two proofs by Marc van Leeuwen there — but if this helped you — great.
May
28
comment On what sets can $\mathfrak{S}_n$ act transitively?
Calling this 'complete classification' is an overstatement, IMHO (just an equivalence of two classification problems).
May
27
comment Prove $\sum_{n= -\infty}^{\infty} \frac{1}{(t+n)^2} = \frac{\pi^2 }{\sin^2(\pi t)}$ using f(x)=1-|x| and Poisson summation formula
Related: Showing $\sum_{n=-\infty}^\infty \frac{1}{(z+n)^2}=\frac{\pi^2}{\sin^2(\pi z)}$ & $\sum\limits_{k = - \infty }^\infty {\frac{{{{\left( { - 1} \right)}^k}}}{{a + k}} = \frac{\pi }{{\sin \pi a}}} $
May
27
comment Spin manifold and the second Stiefel-Whitney class
@QiaochuYuan Sure (the only difference is the first sentences, essentially ;-)
May
26
comment Spin manifold and the second Stiefel-Whitney class
Related: Which manifolds are parallelizable?
May
25
comment Can one prove the existence of tensor product without explicitly constructing it?
Related: Existence proof of the tensor product using the Adjoint functor theorem
May
25
comment Different methods to prove $\zeta(s)=2^s\pi^{s-1}\sin\left(\frac{s\pi}{2}\right) \Gamma (1-s) \zeta (1-s)$.
Related: Contour approach to Riemann zeta functional equation
May
25
comment There does not exist a map $S^2\times S^2\to \mathbb{CP}^2$ with odd degree.
Related: Minimal Degree of map $S^2\times S^2\to \mathbb{CP}^2$