On the degree of regularity of generalized van der Waerden triples

Nikos Frantzikinakis, Bruce Landman, Aaron Robertson

Let $1\le a\le b$ be integers. A triple of the form $(x,ax+d,bx+2d)$, where $x,d$ are positive integers is called an {\em (a,b)-triple}. The {\em degree of regularity} of the f…