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8h
answered Mean or mode of pairwise sum-products over all compositions of an integer
9h
comment Mean or mode of pairwise sum-products over all compositions of an integer
For those for whom the min and max values aren't "clear" (such as myself): $\phi$ is monotone with respect to the partial ordering on composition induced by refinement.
11h
comment Root with bolzano theorem
So split into cases. If it equals $0$, solve the problem by hand; if it doesn't equal $0$, use the theory.
13h
comment Derivative under integral mixed with…
The maker of the problem really shouldn't have used $t$ as the independent variable underlying all the functions and the dummy variable inside the integral.
13h
comment Root with bolzano theorem
Why is that a problem? If it's equal to $0$, then there's your root.
1d
comment How do I solve the triangle?
The points $B$ such that $\angle ABE=\pi/2$ form a circle with diameter $AE$; the points $B$ such that $\angle DBC = \pi/2$ form a circle with diameter $DB$. Try finding $B$ as the point of intersection between those two circles, using either coordinates or geometry.
1d
revised Determine average rate of change of function
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1d
awarded  Peer Pressure
2d
comment The base of S is the triangular region with vertices (0, 0), (3, 0), and (0, 2). Cross-sections perpendicular to the y-axis are semicircles.
Your basic method seems correct. Without having the math formatted in a readable way, though, I'm not motivated to try to find the specific mistake.
2d
comment Using the tangent to the curve to find when it matches another equation
What happens if you calculate the intersection(s) between that parabola and that line?
2d
comment Lower and Upper Triangular Matrices
Do you know already that the inverse of a nonsingular lower triangular matrix is also lower triangular? If so, you can simply write $A=L^{-1}\cdot LA$.
Jan
25
comment Order of any element divides the largest order.
Not yet. First, you treat the case lcm$(m,k)=p$, but you don't consider the case $p<{}$lcm$(m,k)$. Second, your phrase "$t$ is the smallest natural number that fulfills it" is imprecise; and I think when you make it precise, you'll see that what you're claiming isn't necessarily true.
Jan
25
answered Order of any element divides the largest order.
Jan
24
comment Asymptotics of $\sum_{n\leq x}\tau_{k}\left(n\right)$
The step you're worried about is totally fine. You've replaced $\log(x/a)$ with the larger $\log x$, which is valid, and then factored stuff independent of $a$ out of the sum.
Jan
23
comment What proportion of the positive integers satisfy this number-theoretic inequality?
Mits Kobayashi is the expert on such inequalities; I believe one of his recent papers has an algorithm for calculating the proportion you're interested in.
Jan
23
comment A set of integers whose elements all divide $2015^{200}$ but do not divide each other
One way of constructing large examples of such sets is to take $S_k = \{5^p13^q31^r\colon 0\le p,q,r\le200,\, p+q+r=k\}$. You could start by determining which $k$ makes $S_k$ largest; perhaps that's the optimal example. Also a trivial upper bound is $(201)^2$, since if $S$ is larger than that, by the pigeonhole principle it must contain two elements with $p$ and $q$ both equal.
Jan
22
answered Series involving primes
Jan
22
comment Series involving primes
I'm not sure why the downvote ... OP has clearly explained the question being asked and even given a benchmark which he/she would like to improve.
Jan
22
revised Is the set $\{ x\in G | x^{-1}ax=a\}$ is a subgroup of $G$ for any $a\in G$ (where $G$ is a group)?
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Jan
22
answered sucessive primes with distance greater than k