## Three mathematicians that figured it out get to split the $100 prize.

If you thought that your math in high school or college was tough, then you might want to think about the group of mathematicians whose solution to a single math problem takes up 200 terabytes of basic text, and that is with the help of supercomputers!

When you think that a single terabyte can hold over 337,000 copies of War and Peace, an extremely long novel, you can start to understand just how insane this math problem was.

So what was this huge problem and why did we need to know what it is? It is called the Boolean Pythagorean Triple problem, and it was first posed all the way back in the 80s by Ronald Graham.

The problem centers around the Pythagorean formula of a2 + b2 = c2, where a and b are the shorter sides of a triangle, and c is the hypotenuse, or longest side. According to the research, there are specific sets of three positive integers known as Pythagorean triples that can be inserted into the formula, for example: 32 + 42 = 52, 52 + 122 = 132, and 82 + 152 = 172

To think about this, you have to imagine that every integer is painted red or blue.

Graham asked if it was possible to color all of the integers either red or blue so that no set of Pythagorean triples were the same color - a, b, and c. He put $100 up to anyone who could solve it - remember this was the 80s so that was a pretty big deal.

At Popular Mechanics, Andrew Moseman explains why that $100 looks mighty meagre, given the task:

"What makes it so hard is that one integer can be part of multiple Pythagorean triples. Take 5. So 3, 4, and 5 are a Pythagorean triple. But so are 5, 12, and 13. If 5 is blue in the first example, then it has to be blue in the second, meaning either 12 or 13 has to be red.

Carry this logic forward into much bigger numbers and you could see where this would start to get tricky. If 12 has to be red in that 5-12-13 triple, it might force changes down the line that would result in a monochrome triple somewhere."

Mathematicians Victor Marek from the University of Kentucky, Oliver Kullmann from Swansea University, and Marijn Heule from the University of Texas teamed up to figure out whether or not it was possible. They fed a number of techniques into the University of Texas's Stampede supercomputer to narrow down the combination possibilities from 102,300 trillion to 1 trillion.

It took the 800-processor supercomputer 2 days to figure out a solution: 7,824. If you try any more, you can't get the solution that Graham was looking for.

The solution is roughly the size of all of the digitized text that is held by the Library of Congress.