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


Nov
12
awarded  Enlightened
Nov
12
awarded  Nice Answer
Oct
30
awarded  Nice Answer
Sep
30
awarded  Explainer
Sep
24
awarded  Autobiographer
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 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 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
24
reviewed Leave Closed Fibonacci series, which is most pure mathematically?