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Jan
27
awarded  Nice Answer
Jan
26
comment On sets with positive density.
A short answer is No. Try to find a function $f(x)$ such that both sets have positive density.
Jan
26
answered Comparing Euler products
Dec
30
awarded  Good Answer
Dec
15
comment Converse of Chinese Remainder Theorem
The theorem is for the natural injective homomorphism, but I am asking for just isomorphism.
Nov
12
answered Derivative of Analytic Function on Disc Bounded by Integral
Nov
12
comment show that $K/k$ is galois
Since $\theta_2\in k(\theta)= K$, we have $ 1< Aut(K/k)$.
Oct
19
awarded  Nice Answer
Oct
2
answered A non-linear homogeneous diophantine equation of order 3
Sep
8
awarded  Quorum
Aug
29
comment Fractional part of $n\alpha$ is equidistributed
@GerryMyerson You probably meant the "trigonometric polynomials" are dense in the continuous functions.
Aug
27
comment Prove that $\det(I-CD)=\det(I-DC) $
The proof for non-invertible case falls short when the field is not infinite. But, the case can be taken care of by noting that the determinants are polynomials in the entries of matrices.
Aug
27
comment Prove that $\det(I-CD)=\det(I-DC) $
$AB$ and $BA$ has the same characteristic polynomial. This is well-known result.
Aug
27
comment On the number of group homomorphisms from $S_n$ to $S_m$
I think @soloveichik wants to say that there is an injective homomorphism maps $S_{m-1}$ to $S_m$. Thus, we cannot conclude that $n=m$ from $n\leq m$.
Aug
27
comment Commutative rings of order $p^3$.
See this: math.stackexchange.com/questions/368323/…
Aug
24
answered Proving the irrationality of the concatenation of the $n$th powers of primes
Aug
20
comment Primitive polynomials $P$ with $\gcd(P(x),P(y))=1$ for infinitely many $x,y$
Just Fermat's Little Theorem, $x^p -x \equiv x(x-1)\cdots (x-(p-1))$ mod ($p$).
Aug
19
comment $\lim_{n\to\infty} \frac{n}{a_n} = \lim_{x\to\infty} \frac{1}{x}\sharp \{n \leq x: n \in A\}$ when the limit exists.
Take care of $x$ in $a_n < x < a_{n+1}$.
Aug
19
answered Show $\forall \epsilon > 0$ there exists $\delta > 0$ such that $\int_E {|f|d\mu } < \varepsilon $ for all $E\in \cal M$ with $\mu(E) < \delta$
Aug
19
comment is my argument for $\lim_{n\rightarrow\infty}(a_n) = 0$ given $a_n = \tan(n) (\frac{1}{e})^{n}$ correct?
Great! We also have $\sum a_n$ converges.