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Apr
21
comment $[U \cap H : G \cap H] \le [U :G]$
@ClémentGuérin An unfortunate choice of notation by the OP ($U$ being the ambient group). Anyway, my suggestion for the set of left cosets of $U$ modulo $G$ is...ta-daa! $(U/G)_L$ ($L$ stands for "left").
Apr
16
reviewed Approve Positive solutions of $893x - 2432y = 19$
Apr
10
comment Let $A,B$ be two $3\times 3$ matrices with complex entries, such that $BA^2=A^2B$. Prove that $\det(AB-BA)=0$
I have one question: why $3\det(AB-BA)=\mathrm{trace}\bigl[(AB-BA)^3\bigr]$?
Apr
10
comment Let $A,B$ be two $3\times 3$ matrices with complex entries, such that $BA^2=A^2B$. Prove that $\det(AB-BA)=0$
My friend, it seems that you are well aware of the property $\mathrm{trace}(WZ)=\mathrm{trace}(ZW)$. Use this property one more time on your last line!!! (take $W=A, Z=BABAB$).
Apr
3
reviewed Approve A question regarding rational functions being onto.
Apr
3
comment Is there a closed-form of $\sum_{n=1}^{\infty} \frac{\sin(n)}{n^4}$
I would try to work with the imaginary part of the series $\sum_{n=1}^\infty\frac{e^{inx}}{n^4}$, and afterwards to evaluate at $x=1$...I am lazy now, sorry.
Mar
28
reviewed Approve Why are two permutations conjugate iff they have the same cycle structure?
Mar
28
reviewed Reject Matrix can be orthogonally diagonalized iff its eigenvectors are linearly independent
Mar
23
awarded  Revival
Mar
22
answered Is the following set connected given that the union and intersection is connected
Mar
19
comment Find a subring $D$ of ring $D'$ such that: $D'$ is a UFD but not a field, and $D$ is an ID but not a UFD.
ID=Integral Domain?
Mar
13
revised When, how & who first gave this calculation of $\pi$
added 5 characters in body
Mar
12
comment A Dedekind Finite Non-Regular Ring
What is the definition of "Dedekind finite ring"?
Mar
2
revised Multi-index power series
added 7 characters in body; edited title
Feb
17
reviewed Edit Order of an entire function represented as an infinite product
Feb
17
revised Order of an entire function represented as an infinite product
Formatting math; tag
Feb
16
comment Does a non-trivial solution exist for $f'(x)=f(f(x))$?
@Julien I strongly suggest you to explicitly describe the domain of the function on the statement of the problem, something like "Is there some function $f:\mathbb R\to\mathbb R$ other than $0$ satisfying $f'=f\circ f$?"
Jan
24
comment uniform continuity and equivalent sequences
Your definition of equivalent sequences $(a_n)_{n\geq1}$ and $(b_n)_{n\geq1}$ simply says that the difference $a_n-b_n$ tends to $0$ (no matter whether or not each single sequence converges).
Jan
11
answered If $f(x) $ be a polynomial function satisfying $f(x).f(\frac{1}{x})=f(x) +f(\frac{1}{x})$ and $f(4) =65$ then find $f(6)$
Jan
9
comment Functions satisfying $f:\mathbb{N}\rightarrow\ \mathbb{N}$ and $f(f(n))+f(n+1)=n+2$
Problem 11651 of the American Mathematical Monthly is closely related to your problem (see the solution here). Also, see this paper.