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Don't have much time these days...


Oct
28
revised An inequality like Riemann sum involving $\sqrt{1-x^2}$
edited title
Oct
28
revised Existence of lines not containing given points in general position
edited title
Oct
28
revised Lower bound on product of distances from points on a circle
edited title
Oct
28
revised Lower bound on product of distances from points on a circle
added 95 characters in body; added 4 characters in body
Oct
28
revised Lower bound on product of distances from points on a circle
added 178 characters in body
Oct
28
answered Lower bound on product of distances from points on a circle
Oct
28
comment Complex-number inequality $| z_1 z_2 \ldots z_m - 1 | \leq e^{|z_1 - 1| + \ldots + |z_m - 1|} - 1$
I have a feeling it is pretty standard (also supported by the paper stating it as a fact), but I am unable to place where I might have come across it. I had to derive it myself too, though.
Oct
28
comment Complex-number inequality $| z_1 z_2 \ldots z_m - 1 | \leq e^{|z_1 - 1| + \ldots + |z_m - 1|} - 1$
+1: This is what I was about to add!
Oct
28
awarded  combinatorics
Oct
27
comment Iterated polynomial problem
What is the source of this problem? Do you know it, Jaska?
Oct
27
comment Iterated polynomial problem
@svenkat: No, in that case all the P(P(...P(1)...)) are odd.
Oct
27
comment Euler numbers formula
There must be better algorithms than using the formula you state. Perhaps this will have a better algorithm: emis.ams.org/journals/JIS/VOL4/CHEN/AlgBE2.pdf
Oct
27
comment Solving $2x \equiv 1 \pmod{p}$ where $p$ is an odd prime
When p=3, x=2. p=5,x=3. p=11,x=6. p=17,x=9. Do you see any pattern?
Oct
27
comment Do the equations used in Stargate make sense or are they gibberish?
Do you have a link/image?
Oct
27
answered Identity involving Euler's totient function: $\sum \limits_{k=1}^n \left\lfloor \frac{n}{k} \right\rfloor \varphi(k) = \frac{n(n+1)}{2}$
Oct
26
answered Evaluating limit of Summation
Oct
25
comment Bounding the integral $\int_{2}^{x} \frac{\mathrm dt}{\log^{n}{t}}$
@Willie: Marked :-)
Oct
25
comment Bounding the integral $\int_{2}^{x} \frac{\mathrm dt}{\log^{n}{t}}$
@Willie: I just wanted to write how one may have arrived at the answer (which I think would be helpful to someone who comes across it), while the one line clearer proof (which I agree is clearer) gives us no clue whatsoever, as if pulled from a hat :-) The issue about c is minor, IMO.
Oct
25
comment Bounding the integral $\int_{2}^{x} \frac{\mathrm dt}{\log^{n}{t}}$
@Willie: No one is disputing that product rule of derivatives and integration by parts are sides to same coin. I don't understand your issue with c. This is done all the time. You work out some variables you need as you work through, and when you find some values that work, you just present them before hand, to make for a cleaner proof. As to your later comment, I am not making mountains out of anything :-). I just let you know the motivation for posting my answer.
Oct
25
comment Bounding the integral $\int_{2}^{x} \frac{\mathrm dt}{\log^{n}{t}}$
@Willie: The point is that we can start just from the integral without having even the slightest clue about it being $O(x/\log^n x)$. FWIW, I already upvoted your answer, but the fact that we knew the answer and were using that fact bothered me. So I tried to post one where we didn't know the answer beforehand.