View source for Talk:Pythagorean triples

== Confirmation of coprime ==

So perimeter is really easy. Coprime isn't something that people outside of math talk about much. I had to look it up on [[wp:coprime|Wikipedia]] to figure it out, but I'm still not quite sure. It's defined nicely there for two numbers, but we are dealing with three here. Are a, b, and c coprime if gcd(a, b) = gcd(b, c) = gcd(a, c) = 1? Do I need the third gcd evaluation? --[[User:Mwn3d|Mwn3d]] 15:28, 28 June 2011 (UTC)
: Since a^2 + b^2 == c^2, if any two of them are coprime, the third is also coprime to both, so there's no difference how you interpret "coprime" in this situation. --[[User:Ledrug|Ledrug]] 15:50, 28 June 2011 (UTC)
::I see what you did there. So, in general, you need all three gcd's, but in this case (because of the relationship between a, b, and c) you only need two. --[[User:Mwn3d|Mwn3d]] 16:16, 28 June 2011 (UTC)
::: Slight correction: you only need one. --[[User:Ledrug|Ledrug]] 16:18, 28 June 2011 (UTC)

== For reference ==
The correct results:<lang>           10 0 0
          100 17 7
        1,000 325 70
       10,000 4858 703
      100,000 64741 7026
    1,000,000 808950 70229
   10,000,000 9706567 702309
  100,000,000 113236940 7023027
1,000,000,000 1294080089 70230484
</lang> --[[User:Ledrug|Ledrug]] 18:27, 28 June 2011 (UTC)

Hmmm... I get 324 and 4857 for perimeters of 1000 and 10000 respectively. I see that the Python solution also gets 324 for a perimeter of 1000. Am I missing something?--[[User:Tikkanz|Tikkanz]] 23:59, 28 June 2011 (UTC)
:I got 325 for 1000 using Java. Here's the full list: http://pastebin.com/HK74uBCz --[[User:Mwn3d|Mwn3d]] 00:49, 29 June 2011 (UTC)
::Good, beat me to it. I was wondering if I should post the list here, guess not :) --[[User:Ledrug|Ledrug]] 00:52, 29 June 2011 (UTC)
:::I'm running 10K now. Even if it finishes before I get bored I don't think I'll put up the full list. It seems like too much. I'll add the count here in any case. --[[User:Mwn3d|Mwn3d]] 00:54, 29 June 2011 (UTC)
:::It finished immediately after I clicked "submit"... I got 4858 triples and 703 primitives. --[[User:Mwn3d|Mwn3d]] 00:55, 29 June 2011 (UTC)
Ok the goal of the extra, as I stated in task, is not to brute force them.  100k will seriously get on your nerves.  Instead of searching all possible triples, look at the generation section in the WP article, and device a good algorithm to create them: it's a world of difference.  I'll post a solution if everyone gives up, but I really want to have a task where people are required to think a lot. --[[User:Ledrug|Ledrug]] 01:16, 29 June 2011 (UTC)
:Thinking is for Project Euler! Maybe I'll try soon anyway. --[[User:Mwn3d|Mwn3d]] 01:40, 29 June 2011 (UTC)