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Don't have much time these days...


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.
Oct
25
answered Bounding the integral $\int_{2}^{x} \frac{\mathrm dt}{\log^{n}{t}}$
Oct
25
answered How to prove this binomial identity $\sum_{r=0}^n {r {n \choose r}} = n2^{n-1}$?
Oct
25
revised slipping rod on moving truck
added 29 characters in body
Oct
24
comment How to prove $\cos \frac{2\pi }{5}=\frac{-1+\sqrt{5}}{4}$?
Also look up Kastelyn's method on counting the number of tilings of a 2mx2n chessboard with 2x1 rectangles. Choose m=1 and n=2 for this particular problem.
Oct
24
revised Find an infinite set of positive integers such that the sum of any two distinct elements has an even number of distinct prime factors
added 258 characters in body
Oct
24
answered Construction of an infinite set such that any two number from the set are relatively prime
Oct
24
comment Strange Case in Self-Complementary Planarity
This looks like homework. Please consider tagging it as such.
Oct
24
comment Why is $(x^2-2)/(2y^2+3)$ never an integer for any integers $x$ and $y$?
+1: For an interesting question and showing your prior work.
Oct
24
comment Number of integer solutions in [0,10]
Perhaps we can close this as a dupe of math.stackexchange.com/questions/4632/… or maybe math.stackexchange.com/questions/4643/…
Oct
23
comment Taylor series of $\sqrt{1 + x^2}$
This looks like homework. Please consider tagging it as homework.
Oct
23
comment Find an infinite set of positive integers such that the sum of any two distinct elements has an even number of distinct prime factors
@Qiaochu: Thanks, I was thinking that that would be a hard homework problem and hence gave a hint for the possibly easier part of proving existence! I have deleted my answer.
Oct
23
awarded  Citizen Patrol