Yesterday I told you about one of the deepest problems in arithmetic. Today I’ll explain how you can help solve it.
We’re on the hunt for ABC triples. A brief recap: We start with an equation of the form A+B = C, where A, B and C have no factors in common. We find all the primes that divide A, B or C, multiply them together and call the result D. The goal is to find examples where C is bigger than D.
If I start with 2+243=245, the primes are 2 (which divides 2), 3 (which divides 243), 5 (which divides 245) and 7 (which also divides 245), so D = 2 x 3 x 5 x 7 = 220, and C (that is, 245) is bigger than D. Success! We’ve found an ABC triple.
We want more. A full understanding of ABC triples would allow us to solve some of the hardest open problems in arithmetic. More importantly, the reason we’d be able to solve those problems is that we’d understand arithmetic itself a whole lot better.
The first step is to find a whole lot of examples to help researchers guess at the underlying patterns.
That’s where you come in.
You could, of course, sit up late with a pad and a pencil checking examples. But any example small enough to be checked by hand has probably been found already. So if you want to contribute meaningfully to this project, what you really need is a computer. Fortunately, you’ve probably got one.
Now all you need to do is join the ABC@home project, being run by mathematicians at the University of Leiden. You install some software on your computer, and—at times when you aren’t using your computer anyway, or when you’ve got extra processing power you’re not using—it checks for examples and sends the results back to Leiden. As soon as you return to your keyboard, or need your processing power back, the software relinquishes control right back to you (just like a screen saver). You won’t even notice it’s there. And the whole thing is centrally coordinated so your computer is always exploring new territory, as opposed to duplicating someone else’s efforts.
Best of all (at least by some measures), you’ll have the opportunity to bring a bit of glory to this blog. Participants have the option to join “teams”, and teams compete (for nothing more tangible than glory, alas) to find the best examples. I am delighted that blog reader Matthew Lesich has taken the initiative to organize a Team Landsburg(!!)
So: Here’s how to play. First download and install the BOINC software that will run silently in the background on your computer. (Non-Windows users download from here.) During the installation process, you might be asked to reboot. At some point, you’ll be asked to choose a project. Choose ABC@home (which as of now is at the top of the list).
Now, if you’re willing to be publicly associated with the rest of us, go to the Team Landsburg page and click “join”, entering the email address and password that you’ll have chosen during the installation process. And that’s it. From here, everything happens automatically.
I’ll report back periodically on how we’re doing.