Using the algebraic structure of the Stone-Čech compactification of the integers, Furstenberg and Glasner proved that for arbitrary
k
∈
N
k\in \mathbb {N}
, every piecewise syndetic set contains a piecewise syndetic set of
k
k
-term arithmetic progressions.
We present a purely combinatorial argument which allows us to derive this result directly from van der Waerden’s Theorem.