20090424, 18:04  #34 
Aug 2006
5,987 Posts 
An array of ints would probably be faster, if you were willing to use 4 times the memory. Of course going above the 24 GB watermark might cause things to slow down; I'm not sure.
A bitarray might actually be faster than an array of bytes, and it's easy to use in C#: System.Collections.BitArray. This would probably reduce memory use below 500 MB. 
20090425, 09:20  #35 
Sep 2004
215_{16} Posts 
I was wondering if you did something like that to get my source. I will trim it up a bit and post it tomorrow I guess on the website. I am not just storing a 0 or 1, I am storing a 0255, to signify which part of the space the collision is in. Just because a^x + b^y mod n1 and mod n2 are both in the hashtable isn't a real solution unless they are both equal to the same c^z (even then it still wouldn't have to be, because they are only equal mod n1 & n2).
I tried using a int array, but it was slower. I would think that on a 64 bit computer long would be the fastest, but it wasn't. Maybe I wasn't doing it right. I should try a BitArray collections as an additional presieve that is smaller and might be faster. Last fiddled with by Joshua2 on 20090425 at 09:21 
20090425, 19:03  #36 
"Robert Gerbicz"
Oct 2005
Hungary
3^{2}·179 Posts 
A "very" close hit:
(9^4280+7639^1052)/2471^1204 = 0.9999999999946931842701194196 
20090425, 20:04  #37 
Sep 2004
215_{16} Posts 
How did you come up with that? That would be in a range that hasn't been searched before. It isn't likely to find a solution with such big exponents, thats why I'm concentrating on the smaller ones first.

20090425, 21:02  #38  
"Robert Gerbicz"
Oct 2005
Hungary
3^{2}×179 Posts 
Quote:
This is using a new idea: sort the powers in increasing order (store only their logarithms) and use that if a^x+b^y=c^z, then 1/2*c^z<=b^y<c^z (if we assume that a^x<=b^y), if we fix c^z then there is not too much cases for b^y and then it is a simple math to get the logarithm of a^x. This is faster then the old mod tricks. By the builtin eps=1e10 the code is good up to bound=10^4. I haven't checked this, only started, then stopped, it would take about a day. It prints the close values to ki.txt file in a,x,b,y,c,z order one number in each line (consecutive sets are sepearted by a blank line). Not tested too much. Note that i'm checking only gcd(a,b)=1, so it is possible that i'm printing a close hit for that gcd(a,c)>1 or gcd(b,c)>1 (obviously for a solution gcd(a,b)=1 if and only if gcd(a,b,c)=1). And I excluded a,b,c=1 values (it is proven that those are not giving solutions, see Catalan's conjecture/theorem), because that are generating lots of errors in the code. // needs about 1.5 GB Ram for n=10000 Last fiddled with by R. Gerbicz on 20090425 at 21:03 

20090426, 22:49  #39 
Sep 2004
533_{10} Posts 
Nice. How long does it take to check all numbers a,b,c,x,y,z up to 1000? My program takes about an hour on my computer. When you talk about bound, is that checking all variables exactly up to the bound?
BTW this isn't a senior project, its a sophmore project for my AA at a community college. I think I get why a solution gcd(a,b)=1 if and only if gcd(a,b,c)=1, but I read it works for a,c or b,c as well. It seems these two are the same case, but I wasn't exactly sure how this would be proved, and I wanted to double check. 
20090426, 23:05  #40  
"Robert Gerbicz"
Oct 2005
Hungary
3^{2}×179 Posts 
Quote:


20090502, 03:58  #41 
Sep 2004
215_{16} Posts 
I got it to compile w/ Visual Studio 2008 c++, just had to make a (double) conversion explicit. So I don't really know c++; where does your program spend most of its time? Could you provide me a slightly more detailed explanation of what it does, because I would like to implement it in C#.

20090715, 01:24  #42  
"Sastry Karra"
Jul 2009
Bridgewater, NJ (USA)
3^{3} Posts 
Quote:
I am tackling to get a counterexample in two ways. I wrote a JAVA program that gathers the data. Right now, I am gathering data upto 9999 integers on my laptop. Once its done, then I will run another JAVA code to review the data and find if there is atleast one set of numbers as a counter example. Sastry Karra 

20090716, 19:12  #43  
Feb 2004
France
3×311 Posts 
C vS Java
Quote:
T. 

20091018, 00:09  #44 
Sep 2004
1000010101_{2} Posts 
http://jjoshua2.googlepages.com/beal
I published the C# source code there towards the bottom of the page. 
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