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Jul
9
revised $A^\mathrm{T}A=B^\mathrm{T}B \Leftrightarrow \exists$ orthogonal $Q$ such that $A=QB$?
added 6 characters in body
Jun
11
comment A question on Groups and Galois Theory
Since the ground field is not specified, an approach is using the fact: Finite fields have cyclic extension of any degree.
Jun
11
comment A question on Groups and Galois Theory
An idea to avoid WolframAlpha, is the Dirichlet theorem on primes in arithmetic progression.
Jun
10
comment A question on Groups and Galois Theory
@Nishant However, subgroups of $(\mathbb{Z}/n\mathbb{Z})^{\times}$ is not always cyclic. So, just by taking subfield of $n$th cyclotomic field will not be enough.
Jun
10
comment A question on Groups and Galois Theory
The ground field is not specified in the question, so there is much freedom in a sense.
Jun
7
comment Given any integers $a,b,c$ and any prime $p$ not a divisor of $ab$, prove that $ax^2+by^2\equiv c\pmod{p}$ is always solvable.
I answered this before, here
Jun
3
answered $f:\mathbb R \to \mathbb R$ is continuous and lim$_{n\to \infty} f(nx)=0$ for all real $x$ $\implies $ lim$_{x \to \infty}f(x)=0$
Jun
2
comment Convergence of a power series at points where ratio test is inconclusive
Split the $(2n)!$ two parts: product of even numbers which is $2^n n!$, and product of odd numbers $1\cdot 3 \cdots (2n-1)$.
Jun
1
answered Convergence of a power series at points where ratio test is inconclusive
Jun
1
comment Convergence of a power series at points where ratio test is inconclusive
Do you mean $(2n)!$ on the denominator?
Jun
1
comment Finding the sum of a conditionally convergent double series
@Did: There is a slight typo in one of the integral expression of $S$. That should be $\int_0^{\infty} te^{-2t} / (1+ e^{-t})^4 dt$. You have the correct one right after that though.
Jun
1
comment Finding the sum of a conditionally convergent double series
@Did: (+1) Never mind. I know how to justify it now. Thank you anyway.
May
31
comment Prove $\int_0^{\infty}\! \frac{\mathbb{d}x}{1+x^n}=\frac{\pi}{n \sin\frac{\pi}{n}}$ using real analysis techniques only
@RandomVariable This is by $\Gamma(z)\Gamma(1-z)=\pi/\sin(\pi z)$, but how do you get it using only real analysis?
May
31
comment Finding the sum of a conditionally convergent double series
@Did: How can it be justified? Actually you need to change $\sum_m \sum_n \int$ to $\int \sum_m \sum_n$.
May
30
comment Finding the sum of a conditionally convergent double series
Using the first identity requires a justification in changing the order of $\int_0^{\infty}$ and $\sum$.
May
21
revised Prove that there exists an $m$ such that for any $n>m$ there exists at least one prime between $c_n$ and $n$
$x\exp(-c\sqrt x)$ -> $x\exp(-c\sqrt{\log x})$
May
19
comment If $f(3x)=f(x)$ and $f$ is continuous, show that $f(x)$ is a constant function.
If continuity is only assumed for $x>0$, then it is not true. Deleted my previous comment.
May
18
comment Prove that there exists an $m$ such that for any $n>m$ there exists at least one prime between $c_n$ and $n$
I did not care about second statement because you said they are equivalent.
May
13
comment Determinant of a matrix over a field K
Every properties hold true in any fields.
May
13
comment Determinant of a matrix over a field K
What properties of the determinant of a real matrix are you talking about?