Search found 235 matches

by Lord_Farin
Wed Mar 27, 2013 2:38 pm
Forum: News, Suggestions, and FAQ
Topic: New awards.
Replies: 61
Views: 13384

Re: New awards.

3) One thing I would like to see is for the Perfection award to be dynamic. Today, once it's achieved, it remains forever. I think it should change such that all problems (except the latest) are solved. So, there is one week to not lose the award. Same can probably be applied to some of the other a...
by Lord_Farin
Tue Oct 23, 2012 10:25 am
Forum: News, Suggestions, and FAQ
Topic: Forum loading issues
Replies: 5
Views: 1666

Re: Forum loading issues

I have no trouble either. Are you having problems with other sites? It could be your ISP, or some DNS problem.
by Lord_Farin
Fri Aug 31, 2012 9:29 pm
Forum: News, Suggestions, and FAQ
Topic: Functional requests
Replies: 194
Views: 35687

Re: Functional requests

From what I've seen, most problems don't have any PDFs with elegant solutions attached to them. And those that do have such PDFs are more in the easy spectrum. What we need is the opposite: elegant solutions for the hard problems. So here is my idea: What if, once you solve a problem, you gain acce...
by Lord_Farin
Mon Jul 23, 2012 3:40 pm
Forum: News, Suggestions, and FAQ
Topic: Functional requests
Replies: 194
Views: 35687

Re: Functional requests

I always have lights off since I prefer dark backgrounds. This however makes for an ugly display of formulae, as on 334 . A quick check verified that images are used to display TeX. However, here on the forums we have full-fledged TeX in dollar signs enabled. Would it be possible to implement a TeX ...
by Lord_Farin
Mon Jul 23, 2012 6:21 am
Forum: Recreational
Topic: A curiosity discovered while tackling problem 10
Replies: 3
Views: 2482

Re: A curiosity discovered while tackling problem 10

It has already been shown that arbitrarily large prime gaps (difference between consecutive primes) exist. This is stronger observation implies that there are very many intervals of length 100 without a prime.
by Lord_Farin
Thu Jul 05, 2012 12:26 pm
Forum: News, Suggestions, and FAQ
Topic: Optimizing Eratosthenes' Sieve... more?
Replies: 1
Views: 1171

Re: Optimizing Eratosthenes' Sieve... more?

I cut it for three also, but the management is tedious and very hard to get correct.
Obviously, there is a speed effect, and since one needs less memory as well (cutting one third, of course), there is really something to be gained here.
by Lord_Farin
Wed Apr 25, 2012 8:19 pm
Forum: Number Theory
Topic: Mertens function
Replies: 11
Views: 5087

Re: Mertens function

Grouping terms in pairs of two easily gives $a(2n) = -n$, and then it is immediate that $a(2n+1)=n+1$ (you omitted a minus 1 in your $a(5)$, so this is in fact correct). Not sure what $a(n)$ represents, though.
by Lord_Farin
Fri Apr 13, 2012 7:50 pm
Forum: Number Theory
Topic: Euler totient and Mobius function
Replies: 12
Views: 4536

Re: Euler totient and Mobius function

Alhazen wrote:6/(π^2) is the density of squarefree numbers.
What can we do with that?
The squarefree numbers are the ones for which the Möbius function is nonzero.
by Lord_Farin
Wed Mar 07, 2012 9:10 pm
Forum: Number Theory
Topic: Always composite?
Replies: 2
Views: 2016

Re: Always composite?

k = 80, 342 and 848 yield primes (at least, that's what Mathematica says).
by Lord_Farin
Mon Nov 14, 2011 10:00 pm
Forum: Recreational
Topic: Another Time-Travel Paradox?
Replies: 3
Views: 2259

Re: Another Time-Travel Paradox?

In fact, there is a paradox at work here. This is because when assuming FTL (faster-than-light) travel, one necessarily violates the equations of relativity theory. It will therefore be void to discuss about the equation $E = m c^2$ (which as you mentioned, already disposes of conservation of mass; ...
by Lord_Farin
Wed Oct 26, 2011 6:09 am
Forum: Number Theory
Topic: Numbers of the form (1+cX)^1/2
Replies: 8
Views: 3260

Re: Numbers of the form (1+cX)^1/2

You may want to consider this factorisation: z^2 = 1 +cx cx=z^2-1 cx=(z-1)(z+1) For example, suppose c is a prime p. => p|(z-1) or p|(z+1) =>z=kp+1 or z=kp-1 gives all the solutions. (Solutions for x given by x=(z-1)(z+1)/c) If c is composite, then you could consider all factorisations c=a.b You ca...
by Lord_Farin
Tue Oct 25, 2011 1:26 pm
Forum: Number Theory
Topic: Numbers of the form (1+cX)^1/2
Replies: 8
Views: 3260

Re: Numbers of the form (1+cX)^1/2

You should check out some of the theory on quadratic residues. I suspect they will be at least of some help', as they reduce your equations modulo some primes. Further solving then may be easier.
by Lord_Farin
Sun Oct 23, 2011 3:43 pm
Forum: Clarifications on Project Euler Problems
Topic: Problem 354
Replies: 20
Views: 6672

Re: Problem 354

It was helpful for me to realise that the side lengths of the hexagon are 1. This is not the same as the distance between two adjacent hexagons' center points being 2.
by Lord_Farin
Tue Oct 18, 2011 5:25 pm
Forum: Combinatorics
Topic: Balls in finite buckets
Replies: 8
Views: 4689

Re: Balls in finite buckets

Lord_Farin wrote:This might have a running time proportional to $n^2$ or $n^{\frac 3 2}$, or something like that. I think it's more than $n$.
The $n$'s in this sentence should all be $k$'s. I apologise.
by Lord_Farin
Mon Oct 17, 2011 4:22 pm
Forum: Combinatorics
Topic: Balls in finite buckets
Replies: 8
Views: 4689

Re: Balls in finite buckets

I would say your expression for $m > k$ is correct. (That has to count for something) When $n > k$, you can maybe do DP for integer partitioning (into non-negative integer summands) and correct it a bit to suit with the fact that you have $n$ distinguishable buckets. This might have a running time p...
by Lord_Farin
Fri Oct 07, 2011 7:35 am
Forum: News, Suggestions, and FAQ
Topic: Website update Saturday 24 September 2011
Replies: 291
Views: 67280

Re: Website update Saturday 24 September 2011

Such is the case; thanks. EDIT: However, I now see the time correctly (3:18 pm), but still two minor things: 1) The next update is scheduled at 3pm. Hopefully, I will not have to wait for almost an entire day... DST? 2) In the Netherlands, it is more common to use 24-hour clocks. An option for that ...
by Lord_Farin
Thu Oct 06, 2011 11:02 pm
Forum: News, Suggestions, and FAQ
Topic: Website update Saturday 24 September 2011
Replies: 291
Views: 67280

Re: Website update Saturday 24 September 2011

I just noticed that the time zone specified does not include a daylight saving time option (and GMT does not have this). This prevents me from choosing the correct (GMT+2) Amsterdam setting.
by Lord_Farin
Thu Oct 06, 2011 2:40 pm
Forum: News, Suggestions, and FAQ
Topic: Website update Saturday 24 September 2011
Replies: 291
Views: 67280

Re: Website update Saturday 24 September 2011

May you please include the "remember me" feature at login, it's painful to login every time I visit it... After the many requests you will be please to see that I have included a "Remember me at this computer" option on the Login page. Thanks Colin. I appreciate your effort to interpret feedback. I...
by Lord_Farin
Tue Sep 27, 2011 8:50 pm
Forum: News, Suggestions, and FAQ
Topic: Activation code
Replies: 3
Views: 1410

Re: Activation code

Check your spam folder; it might help.
by Lord_Farin
Mon Sep 26, 2011 7:01 am
Forum: Recreational
Topic: Understanding the Universe
Replies: 14
Views: 5656

Re: Understanding the Universe

So my conclusion is: Although illogical: at some moment something need have come out of nothing. Postponing that conclusion is throwing dust into your own eyes. I find it very interesting that you accept illogical conclusion while there could also be explanations that our collective ignorance does ...