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Jan
3
comment Ramanujan-type trigonometric identities with cube roots, generalizing $\sqrt[3]{\cos(2\pi/7)}+\sqrt[3]{\cos(4\pi/7)}+\sqrt[3]{\cos(8\pi/7)}$
Related: upd. in math.stackexchange.com/q/102736 and math.stackexchange.com/a/31600
Jan
3
comment Ramanujan-type trigonometric identities with cube roots, generalizing $\sqrt[3]{\cos(2\pi/7)}+\sqrt[3]{\cos(4\pi/7)}+\sqrt[3]{\cos(8\pi/7)}$
I'll try to expand this answer later
Jan
3
comment More on primes $p=u^2+27v^2$ and roots of unity
(Looks like we already have all pieces of the puzzle and they start to fit together... — but I haven't yet solved it...)
Jan
3
comment More on primes $p=u^2+27v^2$ and roots of unity
and your $k$ is always an element of order $(p-1)/3$ in $\mathbb Z/p^\times$, I guess
Jan
3
comment More on primes $p=u^2+27v^2$ and roots of unity
(and math.stackexchange.com/q/31485 is, of course, related)
Jan
3
comment More on primes $p=u^2+27v^2$ and roots of unity
cf. statement in the upd. of math.stackexchange.com/q/102736
Jan
3
comment Manifold with $\pi_1(M)=F_n$
when you say 'manifold' you mean compact w/o boundary, I guess?
Jan
3
comment What is the least number $n$, such that $n^{2015}+2015$ is prime?
related: math.stackexchange.com/q/663884
Jan
3
comment Show that $\mathbb{R} P^3$ is not homotopy equivalent to $\mathbb{R} P^2 \vee S^3$.
...or compute $\pi_2$
Jan
3
comment How do I evaluate $\sum_{r=1}^{n} [r(r+1)(r+2)(r+3)] $?
Compute answers for small $n$. Then try to guess the general answer. Then try to prove it.
Jan
3
comment A counter example in obstruction theory
@Qiaochu This was x-posted to MO and answered there ($X=\mathbb RP^3$, $Y=\mathbb RP^2$)
Jan
1
comment Combinatorial definition of Hall–Littlewood polynomials (sum over SSYT?)
To me GZ-patterns are as good as SSYT (the bijection is straightforward anyway) — thank you, I'll take a look!
Jan
1
comment Why is $\,c^2-2bcd+b^2d^2=(c-bd)^2\,$?
have you tried just multiplying $c-bd$ by $c-bd$?
Dec
31
comment Proving $S^{4}/G$ is simply connected where $G$ is not a free group action
Your space is $\Sigma(S^3/G)$ — so it's simply connected.
Dec
31
comment Continuous bijection from $\mathbb{R}^n$ to $\mathbb{R}^m$
See en.wikipedia.org/wiki/Invariance_of_domain (there are also numerous discussions of it here on Math.SE)
Dec
31
comment Alternative proof of Wedderburn's little theorem
If you have a new question, please ask it by clicking the Ask Question button. Include a link to this question if it helps provide context.
Dec
31
comment A three variable binomial coefficient identity
LHS is $\sum\binom{i+j}i\binom{n-i}j\binom{n-j}i$. So the question about $\sum\binom{n-i}j\binom{n-j}i$ looks (somewhat) related.
Dec
31
comment Minimum of $\newcommand{\b}[1]{\bigl(#1\bigr)} \newcommand{\f}{\frac} \b{\f3a-1}^2+\b{\f ab-1}^2+\b{\f bc-1}^2+(3c-1)^2$
@ADG could you please add some better tag(s) [than 'unknown']?
Dec
31
comment Polynomial with a root modulo every prime but not in $\mathbb{Q}$.
Actually, I don't know (beside quadratic case). You might want to ask a separate question.
Dec
31
comment Polynomial with a root modulo every prime but not in $\mathbb{Q}$.
related: is there an irreducible polynomial that has a root modulo every prime?