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28m
comment Counting 3-digit integers divisible by 6 but not by 9
You want to consider the numbers modulo $18$. In each block of eighteen, there are two divisible by $9$, out one of these is odd, and gives no problem; and in that block, there are three that are divisible by $6$, but one of them is also divisible by $9$. You should be able to take it from there.
37m
comment What is $0^{i}$?
@soultrane, what you say is surely correct, and maybe we can say that it isolates somewhat the reason for nonconvergence.
17h
comment Determine the group of Automorphisms of $\mathbb{Q}(\zeta_8)$, where $\zeta_8=\exp(2\pi i/8)$
Its Galois group is not isomorphic $\Bbb Z/4$, but rather $(\Bbb Z/8)^\times$, which is isomorphic to $(\Bbb Z/2)^2$.
17h
comment Infinite intersection of open sets need not be open
Take all the open intervals containing $0\in\Bbb R$.
1d
comment Determine the number of subgroups of $\Bbb Z_p \times \Bbb Z_p$, where p is prime.
Every nontrivial subgroup is generated by a nonzero element of $(\Bbb Z/p\Bbb Z)^2$. When do two such elements generate the same subgroup?
1d
comment An example of a product of two distinct convergent series that is divergent
What is the product of two series? Did you mean the series whose terms $z_n$ are $x_ny_n$?
1d
comment Find the fixed field of the following subgroup?
Actually, $\Bbb Q(\omega)$ consists of all the elements $p+q\omega+r\omega^2+s\omega^3$. Including the $t\omega^4$ term is not exactly wrong, but it is superfluous.
2d
comment Solve $x + \frac{ 1 }{y+1/3}=38/3$ in the set of natural numbers
And since the left is $\equiv2\pmod3$ while the right is $\equiv0\pmod3$, you get . . .
2d
comment A line avoiding an Algebraic group
Indeed, for the example I constructed, this cone has general point $(st,st^p,st^{p^2})$, and the single polynomial of which this is a zero is $Y^{p+1}-ZX^p$.
2d
comment A line avoiding an Algebraic group
I like this one much better, and also better than the proof I was struggling to construct. In other language than yours, you are taking the cone of $G$ through the origin, and that’s a 2-dimensional subspace.
2d
comment A line avoiding an Algebraic group
Oh wait. My presumed example seems not to like your argument either. I don’t understand why $\mathrm{Im}\varphi$ being a variety forces it to lie in a plane.
2d
comment A line avoiding an Algebraic group
See my answer below, which is really an extended comment to you answer.
2d
comment A line avoiding an Algebraic group
This looks right to me, but I’m no good at AG. Plus one.
2d
comment Which of the following sets is compact, bounded, closed or open and why?
Generally, it’s considered to be uncouth simply to ask questions in this way, without saying how far you’ve gotten on your own. Uncharitable readers might think that this was a homework problem for which you wanted quick answers without doing any of the hard work.
2d
comment Is it correct to say gcd$(r, 0)$? The definition says greatest common divisor of nonzero integers.
It’s tradeeshun, @egreg.
Feb
11
comment Trace of an algebraic number
I’m not sure, but maybe if you try the companion matrix of $\alpha$ (and it made things really hard for this geezer when you used $\alpha$ for the root and $a_i$ for the coefficients of its minimal polynomial). Indeed, the companion matrix seems to be the key. A real mess, though.
Feb
11
comment An example of the set of distances of two points in two different closed sets having no infimum
Try the $x$-axis in $\Bbb R^2$ and something that’s closed but unbounded.
Feb
10
comment Is this polar equation correct?
You need to use the proper recipe for calculating area in polar coordinates.
Feb
6
comment Need help in verifying if I am taking the derivative of $f(x) = \frac{x}{\cos(x)}$ correctly
Not correct. At first glance, it seems to me that you’re trying to force your function into the chain-rule category.
Feb
5
comment Finding Galois Group
Since the extension is not normal, maybe you’re asking for the Galois group of its normal closure over $\Bbb Q$?