Arithmetic Progressions of Length Three in Multiplicative Subgroups of ${\mathbb{F}}_p$

In this paper, we give an algorithm for detecting non-trivial 3-APs in multiplicative subgroups of ${\mathbb{F}}_p^{\times }$ that is substantially more efficient than the naive approach. It follows that certain Var der Waerden-like numbers can be computed in polynomial time.