William J. Wesley, An elementary solution to the 2-color Pythagorean triples problem

In the 1980s, Ron Graham asked whether every red/blue coloring of the positive integers contains a monochromatic Pythagorean triple and offered a $100 prize for the answer. The bounty was claimed in 2016 by Heule, Kullmann, and Marek, who showed that every such coloring of [1,7825] has a monochromatic triple. Their proof used SAT solvers and took over 50,000 CPU hours to produce and verify. In this talk we will present an elementary solution to Graham’s problem that requires neither deep analytic arguments nor extensive computation.