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8h
answered Cyclic consecutive zeros of binary sequence with prime length
1d
comment In how many ways can the integers from $1$ to $n$ be divided into two groups with the same sum?
A search on the Online Encyclopedia of Integer Sequences yields entry oeis.org/A063865 , which tells you various ways to compute this number as well as an asymptotic formula for it.
1d
comment Differentiating expression involving summation
I don't doubt it; I explained why.
1d
answered Prove that the denominators of the $10^n$th Harmonic Numbers divided by $10^n$ converge to $\log_{10} e$
1d
comment Determine if the following linear transformation is surjective or injective
he or she......
1d
answered Differentiating expression involving summation
2d
comment Trigonometric identity reduction
Try writing $\cos\theta=\frac12(e^{i\theta}+e^{-i\theta})$ and $\sin\theta=\frac1{2i}(e^{i\theta}-e^{-i\theta})$, expanding everything like crazy, and reassembling the pieces to a reduced form. (You can practice this procedure on the first identity to see how it goes, then try it on the expression you want.)
May
22
comment Show that subspace metric induces subspace topology
That's good—it tells you where you need to concentrate your efforts. There's no point in trying to complete a proof of the above statement (or even to follow someone else's proof) if you don't understand the definitions of the nouns involved. Start by thinking about this: what are the open sets in $X$? What do they have to do with the metric $d$? Then you can proceed to thinking about what the induced metric on $A$ is, what topology it induces, and what the subspace topology on $A$ is.
May
21
comment Show that subspace metric induces subspace topology
James wrote: take a "metric open" set in A, and try showing it is a "subspace open" set. What part of this do you need more explanation for? Do you understand the definitions of the two types of sets, or not?
May
21
accepted Lebesgue measures defined on subspaces of $\Bbb R^n$
May
21
comment What is real $R$ so that every subset of Euclidean space with diameter one is inside a ball of radius $R$?
Do you have an example in mind showing that the answer can't be smaller than $\sqrt2$?
May
21
comment Estimate of sum of divisors up to a certain number?
Good question!—I can't immediately prove (nor disprove) your cojecture. Remark 1: it suffices to consider the case where $n$ divides $\mathop{\rm lcm}[1,2,\dots,k]$, since replacing $n$ by $\gcd(n,\mathop{\rm lcm}[1,2,\dots,k])$ doesn't change $\sigma(n,k)$. Remark 2: the conjecture can be restated as follows. Let $S$ be a set of positive integers closed under taking divisors; then the conjecture is that $\sum_{d\in S} d \le \max S \cdot c(\ln\mathop{\rm lcm}S + 1)$.
May
21
comment How to evaluate the determinant
If you add any column to another column, a row operation will suggest itself....
May
20
comment Is there a counterexample? $\forall p \in \Bbb P\ ,\ p\gt 61\ ,\ \exists\ r1,r2\ \in \{\ Primitive\ Roots\ Modulo\ p\ \}\ /\ r1+r2 = NextPrime(p)$
Yes, that too is likely to be true for all large $n$, by a similar probabilistic heuristic which I will let you discover. Of course, it's a stronger statement than the Goldbach conjecture, as you point out, so it's not likely to be proved any time soon (nor, in my opinion, to lead to fresh insight on the Goldbach conjecture).
May
20
answered Is there a counterexample? $\forall p \in \Bbb P\ ,\ p\gt 61\ ,\ \exists\ r1,r2\ \in \{\ Primitive\ Roots\ Modulo\ p\ \}\ /\ r1+r2 = NextPrime(p)$
May
15
asked Lebesgue measures defined on subspaces of $\Bbb R^n$
May
14
comment Finding the numbers of primes $<n$ by counting sums of two squares
@MikaelJensen : your last question about "these numbers" isn't really possible to answer at this point. You have hinted at the description of a set of integers (certain sums of two squares), but you haven't given enough information to specify exactly what set you're talking about.
May
14
comment Finding the numbers of primes $<n$ by counting sums of two squares
First of all, I don't think you mean what you wrote in the first sentence. Second, the OP seems to be describing some sort of sieving on the set of sums of two squares, so its full counting function is presumably not directly relevant to $\pi(x)$.
May
14
comment conformal map disc with two removed points
I doubt that there is.
May
13
comment conformal map disc with two removed points
One path to a solution is to argue that any such map can be extended continuously to a map from the open unit disk to itself (i.e., that it has "removable singularities" at $\pm\frac12$). Then you can use what you know about the automorphisms of the unit disk.