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location Moscow, Russia
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visits member for 4 years, 2 months
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umagon at google mail


Aug
29
awarded  Announcer
Aug
8
reviewed Looks OK To find the logarithm of $1728$ to the base $2 \sqrt{3}$
Aug
1
comment Does there exist a cubic polynomial $f(x)$ such that $f(x)\equiv0 \pmod p $ has no integer solutions if $p\equiv 3\pmod 4$?
Oh, you're right, for finite fields the Galois group can't be $S_3$...
Aug
1
comment Does there exist a cubic polynomial $f(x)$ such that $f(x)\equiv0 \pmod p $ has no integer solutions if $p\equiv 3\pmod 4$?
No, the question doesn't require the polynomial to have a root mod all p=4k+1 — and since 1/3<1/2 I don't see an immediate contradiction with Chebotarev's theorem.
Aug
1
comment Does there exist a cubic polynomial $f(x)$ such that $f(x)\equiv0 \pmod p $ has no integer solutions if $p\equiv 3\pmod 4$?
Ah, I see. But IMHO the question asks about a cubic polynomial that (like $x^2+1$) doesn't have zeroes mod all primes of the form $4k+3$.
Aug
1
comment Does there exist a cubic polynomial $f(x)$ such that $f(x)\equiv0 \pmod p $ has no integer solutions if $p\equiv 3\pmod 4$?
@gammatester p=3 is not 1 mod 3
Jul
27
reviewed Leave Closed A persisting element in all subgroups.
Jul
26
reviewed Looks OK Prove that $s_n \leq 1+\ln n$, where $s_n$ is the $n$th partial sum of the harmonic series
Jul
26
reviewed Close Prove that $16 \cos 12^\circ ·\cos 24^\circ ·\cos 48^\circ· \cos 96^\circ ·\cos 192^\circ = 1$
Jul
26
reviewed Leave Closed Solve $e^x-1= 2x$ with numerical or analytical methods.
Jul
26
reviewed Looks OK Convergence of $a_n=1+1/5+1/9+\ldots+\frac{1}{4n-3}$
Jul
25
reviewed Looks OK Proving an expression is composite
Jul
25
reviewed No Action Needed Do all primes $p$ except 2 and 3 divide the sum of the squares of integers from 0 to $p - 1$?
Jul
25
reviewed Looks OK Find two functions given properties of their limits
Jul
25
reviewed Leave Closed Prove that: $\frac{1}{11+a^2}+\frac{1}{11+b^2}+\frac{1}{11+c^2}+\frac{1}{11+d^2} \leq \frac{1}{3}$
Jul
25
reviewed Leave Closed Solve for x: sin2 x − cos2 x = sin x, −π ≤ x ≤π
Jul
25
reviewed No Action Needed Does this property of normal subgroups have a name?
Jul
25
reviewed Close Simplify $\sec(x + \pi/2)$
Jul
24
reviewed Leave Closed Fibonacci series, which is most pure mathematically?
Jul
24
revised The Name for $\mathbb{R}$, $\mathbb{C}$, $\mathbb{H}$ and $\mathbb{O}$ Exclusively Algebras?
edited tags