Boolean Pythagorean triples problem

The Boolean Pythagorean triples problem was a conjecture relating to Pythagorean triples which was shown to be false using a Computer-assisted proof in May 2016.

The problem asks if it is possible to color all the integers either red or blue so that no pythagorean triple of integers a, b, c, satisfying $a^{2}+b^{2}=c^{2}$ are all the same color. The proof tested all possible colouring of numbers up to 7,825 and found no such colouring was possible. There are 10^2,300 such colourings and the proof took two days of time on the Stampede supercomputer at the Texas Advanced Computing Center. The proof generated 200 terabytes of data.

In the 1980's Ronald Graham offered a $100 prize for the solution of the problem, which has new been awarded to the three researchers. The proof was published on arXiv on 3 May 2016.