## Search found 235 matches

- Wed Mar 27, 2013 2:38 pm
- Forum: News, Suggestions, and FAQ
- Topic: New awards.
- Replies:
**68** - Views:
**32886**

### 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...

- Tue Oct 23, 2012 11:25 am
- Forum: News, Suggestions, and FAQ
- Topic: Forum loading issues
- Replies:
**5** - Views:
**3052**

### 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.

- Fri Aug 31, 2012 10:29 pm
- Forum: News, Suggestions, and FAQ
- Topic: Functional requests
- Replies:
**194** - Views:
**62647**

### 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...

- Mon Jul 23, 2012 4:40 pm
- Forum: News, Suggestions, and FAQ
- Topic: Functional requests
- Replies:
**194** - Views:
**62647**

### 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 ...

- Mon Jul 23, 2012 7:21 am
- Forum: Recreational
- Topic: A curiosity discovered while tackling problem 10
- Replies:
**3** - Views:
**3963**

### 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.

- Thu Jul 05, 2012 1:26 pm
- Forum: News, Suggestions, and FAQ
- Topic: Optimizing Eratosthenes' Sieve... more?
- Replies:
**1** - Views:
**1857**

### 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.

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.

- Wed Apr 25, 2012 9:19 pm
- Forum: Number Theory
- Topic: Mertens function
- Replies:
**11** - Views:
**8780**

### 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.

- Fri Apr 13, 2012 8:50 pm
- Forum: Number Theory
- Topic: Euler totient and Mobius function
- Replies:
**12** - Views:
**8014**

### Re: Euler totient and Mobius function

The squarefree numbers are the ones for which the Möbius function is nonzero.Alhazen wrote:6/(π^2) is the density of squarefree numbers.

What can we do with that?

- Wed Mar 07, 2012 9:10 pm
- Forum: Number Theory
- Topic: Always composite?
- Replies:
**2** - Views:
**3449**

### Re: Always composite?

k = 80, 342 and 848 yield primes (at least, that's what Mathematica says).

- Mon Nov 14, 2011 10:00 pm
- Forum: Recreational
- Topic: Another Time-Travel Paradox?
- Replies:
**3** - Views:
**3848**

### 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; ...

- Wed Oct 26, 2011 7:09 am
- Forum: Number Theory
- Topic: Numbers of the form (1+cX)^1/2
- Replies:
**8** - Views:
**5677**

### 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...

- Tue Oct 25, 2011 2:26 pm
- Forum: Number Theory
- Topic: Numbers of the form (1+cX)^1/2
- Replies:
**8** - Views:
**5677**

### 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.

- Sun Oct 23, 2011 4:43 pm
- Forum: Clarifications on Project Euler Problems
- Topic: Problem 354
- Replies:
**21** - Views:
**15971**

### 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.

- Tue Oct 18, 2011 6:25 pm
- Forum: Combinatorics
- Topic: Balls in finite buckets
- Replies:
**8** - Views:
**6835**

### Re: Balls in finite buckets

The $n$'s in this sentence should all be $k$'s. I apologise.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 $n$.

- Mon Oct 17, 2011 5:22 pm
- Forum: Combinatorics
- Topic: Balls in finite buckets
- Replies:
**8** - Views:
**6835**

### 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...

- Fri Oct 07, 2011 8:35 am
- Forum: News, Suggestions, and FAQ
- Topic: Website update Saturday 24 September 2011
- Replies:
**291** - Views:
**106666**

### 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 ...

- Fri Oct 07, 2011 12:02 am
- Forum: News, Suggestions, and FAQ
- Topic: Website update Saturday 24 September 2011
- Replies:
**291** - Views:
**106666**

### 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.

- Thu Oct 06, 2011 3:40 pm
- Forum: News, Suggestions, and FAQ
- Topic: Website update Saturday 24 September 2011
- Replies:
**291** - Views:
**106666**

### 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 i...

- Tue Sep 27, 2011 9:50 pm
- Forum: News, Suggestions, and FAQ
- Topic: Activation code
- Replies:
**3** - Views:
**2491**

### Re: Activation code

Check your spam folder; it might help.

- Mon Sep 26, 2011 8:01 am
- Forum: Recreational
- Topic: Understanding the Universe
- Replies:
**14** - Views:
**8724**

### 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 ...