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location Moscow, Russia
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visits member for 4 years, 6 months
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Jan
18
reviewed Close Associative Property for Composition of Functions
Jan
18
reviewed Close How do I mathematically explain this relationship?
Jan
18
reviewed Close Help with Theorem III.3.11 in Hungerford's algebra book
Jan
18
reviewed Close Simplifying a complex number
Jan
18
reviewed Close How to prove that?
Jan
18
reviewed Close Sum of primes up to p is multiple of p?
Jan
18
reviewed Close How many pairs of integers $(A, B)$ are there in the range $[1,\ldots, N]$, such that $\gcd(A,B) = B$?
Jan
18
reviewed Close Smallest natural number $x$ that is twice a perfect square, three times a perfect cube, and five times a perfect fifth power
Jan
18
reviewed Close If $\sum_{n=1}^{\infty}|a_n|$ and $\sum_{n=1}^{\infty}|b_n|$ converge, does $a_k/b_k$ converge?
Jan
18
reviewed Close Number of k for which we have reducible polynomial
Jan
18
comment Does the limit or the infinite sum of $\binom{z+r-1}{z}$ converge?
Re: «Which will tend to one I think» — no, why? It's always greater than $r$, for example (assuming $z$ is a positive integer).
Jan
18
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.
Jan
17
revised Calculate all the generators in $\mathbb{Z}/61$
edited tags
Jan
17
comment Showing ${n + a - 1 \choose a - 1} = \sum_{k = 0}^{\left\lfloor n/2 \right\rfloor} {a \choose n-2k}{k+a-1 \choose a-1}$
cf. math.stackexchange.com/q/601940 etc
Jan
17
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...
Jan
17
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...
Jan
17
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 $\sum \binom nlx^l$?
Jan
17
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).
Jan
17
reviewed Reviewed Solve the equation $\frac1{2x}+4=x-1$ for $x$
Jan
16
reviewed Leave Closed $\mathcal A$ is empty, what is $\bigcap_{S\in\mathcal A}S$?