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May
15
comment Totally busted euler trail.
In 1), you seem to be using a definition where a trail must end where it begins, but I don't think that's the usual definition.
May
15
comment Sum of squared/cubed combinations
Has anyone looked the sequence up in the Online Encyclopedia of Integer Sequences?
May
15
comment question on subgroups of prime order
Kamal, some of us get annoyed when people copy-paste questions from unidentified sources without giving any indication of why they want to answer the question, or whether they have done any work, or what they know about the question. Questions like this run the risk of rapidly getting closed.
May
15
comment If $\operatorname{sp}(A) \cup \operatorname{sp}(B)=\operatorname{sp}(A\cup B) \Rightarrow A\cup B$ is linearly dependent
@Don, I started typing it as an answer, then decided it was really more of a hint as to another way to do the problem, so I made it a comment. But you are welcome to post it as an answer.
May
15
comment $\mathbb{R}^n$ and $\mathbb{Q}^n$: On the Nature of Solutions
I don't see what question you have that hasn't already been answered at the other question.
May
15
comment If $\operatorname{sp}(A) \cup \operatorname{sp}(B)=\operatorname{sp}(A\cup B) \Rightarrow A\cup B$ is linearly dependent
Think about this: the span of $A\cup B$ is a vector space. The union of the span of $A$ and the span of $B$ is a union of two vector spaces. Under what circumstances can the union of two vector spaces be a vector space?
May
15
comment What is $\frac{(an)!}{n!}$?
It can't. Let $a=2$, $n=3$, then your number has a factor $5$, which none of $a!$, $n!$, $a$, or $n$ have.
May
15
revised Modulus Cancellation Law
edited tags
May
15
comment Modulus Cancellation Law
No, @Babak, that only works when $a$ is prime.
May
15
answered How to show that $A=B-C$
May
14
comment $\mathbb{R}^n$ and $\mathbb{Q}^n$: On the Nature of Solutions
Barisa, if there's something you want Don (or me, or anyone else) to do, you'll have to do a better job of explaining exactly what it is you want done.
May
14
comment $\mathbb{R}^n$ and $\mathbb{Q}^n$: On the Nature of Solutions
@Don, yes, I know that $x-y=3$ has solutions in the rationals. But you wrote, "if the non-homogeneous system is defined over the rationals then any real solution is in fact rational," and it seems to me that that is not the case.
May
14
revised Show using induction (coupled linear recurrences)
more informative title
May
14
comment $\mathbb{R}^n$ and $\mathbb{Q}^n$: On the Nature of Solutions
Barisa, what could be more concrete than reducing a matrix by elementary row operations? What do you know about solving systems of linear equations? But @Don, the non-homogeneous system $x-y=3$ is defined over the rationals, yet it has real solutions that are not rational. And a system with irrational coefficients could have a rational solution.
May
14
revised $\mathbb{R}^n$ and $\mathbb{Q}^n$: On the Nature of Solutions
edited tags
May
14
comment Number of ways to arrange $n$ people in a line
Or try calculating $a_1,a_2,a_3,a_4$ or maybe a few more, and then consulting the Online Encyclopedia of Integer Sequences.
May
14
comment Conditions for f(x,y) to coincide with some g(x) + h(y)
The question should be in the body, not the title. Please edit to include the question in the body.
May
14
revised Conditions for f(x,y) to coincide with some g(x) + h(y)
edited tags
May
14
comment Prove that for n~=n' sum is much smaller than the case with n=n'
"What you've said is obvious." This is not the way to encourage people to take an interest in your problem.
May
14
comment Applications of design theory
I don't know what "ordered through a cd" means. The extract is on the page to which I linked, under the heading, "Extract from interview". There is also a link there to the full interview.