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Aug
31
comment In how many ways can three numbers be selected from the numbers $1,2,\dots,300$ such that their sum is divisible by $3$?
In the $(0,1,2)$ case, we can choose $100^3$ triples.
Aug
31
revised Factorising complex equations
edited tags
Aug
31
reviewed Reviewed Want to clarify whether I am correct or not, $\Phi(G) \subseteq \Phi(H)$?
Aug
30
revised A problem on limit
added 137 characters in body
Aug
30
comment For what $n$ can $\pm 1\pm 2\pm 3 … \pm (n-1) \pm n = n+1$?
That's an assertion. Could you add a proof of this assertion into this answer?
Aug
30
comment Find order of $xy$ provided $x^2=e, y^3=e$ and $yxy=xy^2x$
It's somewhat implicit that saying e.g. "$x^2=e$" implies $x$ has order $2$, otherwise we'd instead say "$x=e$" (or not even introduce $x$). Perhaps I'm a bit too pedantic (but this kind of detail matters e.g. for automated theorem proving). Anyway, the answer is fine so I better +1 it.
Aug
30
comment Find order of $xy$ provided $x^2=e, y^3=e$ and $yxy=xy^2x$
Hmm... it could be that $x=e=y$ too (in which case $xy=e$ has order $1$). The question doesn't say e.g. "the order of $x$ is $2$". [It must be a divisor of 3, though. So it's either $3$ or $1$.]
Aug
30
revised Find order of $xy$ provided $x^2=e, y^3=e$ and $yxy=xy^2x$
added 8 characters in body; edited tags; edited title
Aug
29
revised How is $\{ (1/n , 1 + 1/n) \}_{n \geq 1}$ a cover for $(0,2)$?
edited title
Aug
29
comment Problem on directed graph involving $\gcd$
The question for strongly connected digraphs is now here.
Aug
29
comment Problem on directed graph involving $\gcd$
It looks like a counterexample to me. I wonder if this is a homework question; the lecturer might have a surprise when the assignments are returned. (I suppose the theorem would be true if there were no "incoherent" cycles.)
Aug
29
revised Problem on directed graph involving $\gcd$
Added drawing of graph
Aug
29
comment Problem on directed graph involving $\gcd$
What is the value of $p$ if $G$ has no cycles?
Aug
29
comment Calculate the Determinant?
I neatened this answer up a bit, and also corrected the arithmetic.
Aug
29
revised Calculate the Determinant?
Neatened it up; corrected arithmetic.
Aug
28
revised $\frac1a+\frac1b+\frac1c=0 \implies a^2+b^2+c^2=(a+b+c)^2$?
edited tags
Aug
28
revised mean of two consecutive number helps proving both number equals..
edited tags
Aug
28
revised How do I explain the fallacy $\frac00=2$ in this case?
edited tags
Aug
28
revised Critique on a proof by induction that $\sum_{i=1}^n i^2= n(n+1)(2n+1)/6$?
re-titled; re-tagged
Aug
28
revised Simultaneous solution(s) to $a^2+4b^2+4ab=0$ and $a^2+4b^2+32+16a-8b=0$?
re-titled; re-tagged