Ruzsa–Szemerédi problem

The Ruzsa–Szemerédi problem is a question in the field of combinatorial number theory, particularly concerning sets of integers and their structure. It was posed by Hungarian mathematicians Imre Ruzsa and Endre Szemerédi. The problem revolves around the concept of progressions in subsets of integers. Specifically, it asks how large a subset of integers can be if it avoids certain arithmetic progressions of a given length.