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Jul
12
comment Probability of their's constituting a triangle?
...or of math.stackexchange.com/questions/26424
Jul
9
comment Prove that $\sum_{k=0}^{m}\binom{m}{k}\binom{n+k}{m}=\sum_{k=0}^{m}\binom{n}{k}\binom{m}{k}2^k$
related: wiki: Delannoy numbers
Jul
8
comment Elementary, direct proof of when $5$ is a quadratic residue mod $p$
related: Special Cases of Quadratic Reciprocity and Counting Fixed Points
Jun
24
comment Contractible Subspace and Homotopy Equivalence
E.g. $X=S^1$, $A=S^1-pt$.
Jun
20
comment Relation between $K$-theories
Related: Relationship between topological and Quillen's K-theory
Jun
11
comment Help me ID this weird $\pi$ formula
Terms are clearly related to $\binom{1/2}n=(-4)^n\binom{2n}n/(1-2n)$ and $\pi/4$ is of course $(1/2)!^2$. So the identity looks similar to Vandermonde's convolution $\sum_k\binom nk^2=\binom{2n}n$ for $n=1/2$ or smth like that.
Jun
10
comment Example of something easier to count with $q$-analog?
(Re: 'justifying its relation to the gamma function... is more complicated'): the definition of q-gamma is completely analogous to a definition of ordinary gamma-function (the lesser-known-but-easier-to-comprehend one).
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.