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2d
answered What is p(x=1) of this moment generating function?
2d
comment Is this integral $\int_0^1\left(\left\{\frac1x\right\}-\frac12\right)\frac{\log(x)}{x}dx$ equal to zero?
@MhenniBenghorbal Is it without minus sign? I would be surprised if so. In my observation, it keeps decreasing.
2d
comment Is this integral $\int_0^1\left(\left\{\frac1x\right\}-\frac12\right)\frac{\log(x)}{x}dx$ equal to zero?
If you want a "proof of convergence" without any aid of electronic device, you can keep using the Taylor series for $\log (1+x)$ to obtain $O(\log m/ m^2)$.
2d
comment Is this integral $\int_0^1\left(\left\{\frac1x\right\}-\frac12\right)\frac{\log(x)}{x}dx$ equal to zero?
I think it converges to a value close to $-0.0025$.
2d
comment Is this integral $\int_0^1\left(\left\{\frac1x\right\}-\frac12\right)\frac{\log(x)}{x}dx$ equal to zero?
Wolfram Alpha Estimate 1 shows that the sum converges, since each term is $O(\log m / m^2)$. And this one Wolfram Alpha Estimate 2 shows that the sum does not converge to zero.
2d
comment Find the non-trivial solutions of the diophantine equation: $a^3+3a^2b=c^3$
Writing $a^2(a+3b)$ helps.
2d
answered How prove this limit $\left(\frac{1}{2}+\sum_{k=1}^{n-1}(-1)^{\lfloor\frac{mk}{n}\rfloor}\{\frac{mk}{n}\} \right)^n=\frac{1}{\sqrt{e}}$
Aug
13
comment Equidistribution of roots of prime cyclotomic polynomials to prime moduli
I think $S_p = \sum_{k = 1}^{\ell - 1} e(\alpha^{k \cdot \frac{p-1}{\ell}})$ should be $S_p = \displaystyle\sum_{k = 1}^{\ell - 1} e(\alpha^{k \cdot \frac{p-1}{\ell}}/p)$.
Aug
9
answered If $AB+BA=0$ and $B=AX+XB$, then $B$ is nilpotent.
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.