Monochromatic additive-multiplicative Schur pattern for general finite colorings

Establish whether the pattern consisting of positive integers x, y, x+y, and xy is partition regular for every finite coloring of the positive integers, beyond the presently known affirmative result for two-colorings.

Background

The pattern simultaneously imposes additive and multiplicative monochromaticity on the same pair x and y. The paper reports that the problem has an affirmative solution for two-colorings, but remains unresolved for arbitrary finite colorings.