Short Bytes: Three scientists have come up with a solution to Pythagorean triples by running 800 processors in parallel for two days. The resulting file is as big as 200TB of data and beyond a certain number, the Pythagorean puzzle could not be solved.
This puzzle has been long known to the mathematicians. Back in the 1980s, an offer of $100 was made for anyone who could solve this problem by Ronald Graham.
Ronald Graham is a mathematician at the university of California, San Diego. For the offer challenged in the 1980s, the previous record-holder’s had come up with around 13GB of data which was published in 2014.
Pythagorean triples problem statement:
The problem requires to colour each positive integer in two colours, either red or blue, so that no triples of integers a, b and c that satisfy Pythagoras’ famous equation a2 + b2 = c2.
For example, for the Pythagorean triple 3, 4 and 5, if 3 and 5 were coloured blue, 4 would have to be red.
The recent proof paper was posted on arXiv server by three computer scientists named Heule, Oliver Kullmann from Swansea University, UK, and Victor Marek of the University of Kentucky in Lexington.
These three scientists have now shown that there are many allowable ways to colour the integers up to 7,824.
Even though there are more than 102,300 ways to colour the integers up to 7,825, the researchers took advantage of many symmetrical models and techniques from number theory to reduce the total number of possibilities so that the computer had to check under 1 trillion permutations and combinations.
The team ran 800 processors in parallel for two days in the University of Texas’s Stampede supercomputer to find out all the possibilities. The researchers then verified the proof using another computer program.
Also Read: Mathematician Srinivasa Ramanujan: The Man Who Knew Infinity
