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9h
comment Characterizing the Galois group using permutations of roots
Thanks. Okay, so now replace $S_4$ with an arbitrary subgroup $G\leq S_n$. If $G$ satisfies that property, must $G$ be the Galois group? In other words, does that property characterize the Galois group?
14h
comment Characterizing the Galois group using permutations of roots
I edited my question title in the hopes of avoiding an XY problem.
14h
revised Characterizing the Galois group using permutations of roots
added 134 characters in body; edited title
14h
comment Word problem number theory
@labbhattacharjee This is a nitpick, but that doesn't follow directly, does it? I mean, I agree that the LCM divides every common multiple, but you can't deduce that instantly from the fact that it's the smallest one, can you?
15h
comment Word problem number theory
You're using the fact that the LCM divides every common multiple, aren't you?
15h
revised Characterizing the Galois group using permutations of roots
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15h
comment Characterizing the Galois group using permutations of roots
@mt__ I think I may have badly formulated my converse. I'll edit in some more details.
15h
revised Word problem number theory
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15h
comment Word problem number theory
You're sure of it, but you don't know the reasoning behind it?
15h
comment Characterizing the Galois group using permutations of roots
@mt_ So you're saying the converse is in fact true for the full symmetric group?
18h
comment Does this integral have any closed form? $\displaystyle\int\frac{1}{x+\sin(x+1)}\mathop{\mathrm dx}$
Your substitution will turn it into a rational function in $x$ and $\sin(x)$, but I don't think that such a thing is guaranteed to have an elementary closed form.
18h
asked Characterizing the Galois group using permutations of roots
21h
comment Why is $sinx$ the imaginary part of $e^{ix}$?
@EamesCobb Do you at least understand why the trig functions turn up here in the first place?
21h
comment Why is $sinx$ the imaginary part of $e^{ix}$?
Do you specifically want to know why the imaginary part isn't $\cos$?
21h
comment Why is $sinx$ the imaginary part of $e^{ix}$?
Not to be rude, but what does this add that wasn't contained in the other answer?
21h
comment Why is $sinx$ the imaginary part of $e^{ix}$?
The best explanation I've seen goes that since the derivative of $e^{ix}$ is $ie^{ix}$, we have a curve which starts at $1$ and has a "velocity vector" always orthogonal to itself, pointing left, and of magnitude $1$. So naturally, it draws a circle. But I don't know how to make this rigorous.
1d
comment Show that there is no integer n with $\phi(n)$ = 14
(Also, your argument for the prime case is a bit complicated. Assume $n$ is prime, then $n=15$, contradiction!).
1d
comment Show that there is no integer n with $\phi(n)$ = 14
I don't see at all what "similar argument" you're implying for the case when $n$ isn't prime, could you explain?
1d
comment Is $x^4+2$ irreducible over $\Bbb{Q}(i)$?
How do you know it's irreducible in $\mathbb Z_5[x]$?
1d
revised Please advise on the order of calculation
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