Uniform eventown problems

Let n≥k≥l≥2 be integers, and let F be a family of k-element subsets of an n-element set. Suppose that l divides the size of the intersection of any two (not necessarily distinct) members in F. We prove that the size of F is at most (⌊n/l⌋k/l) provided n is sufficiently large for fixed k and l.