Frankl and Wilson proved a certain theorem about set-systems with certain restrictions on their order and the order of their intersections modulo $p$ for $p$ prime, and wrote "it would be interesting to know whether it holds for composite $p$ as well" .
Frankl gave a counterexample for $p=6$, and Grolmusz  gave strong counterexamples for all composite $p$.p$ with at least two prime factors.
 Frankl, P.; Wilson, R. M. Intersection theorems with geometric consequences. Combinatorica 1 (1981), no. 4, 357–368. http://www.ams.org/mathscinet-getitem?mr=647986
 Grolmusz, Vince Superpolynomial size set-systems with restricted intersections mod 6 and explicit Ramsey graphs. Combinatorica 20 (2000), no. 1, 71–85. http://www.ams.org/mathscinet-getitem?mr=1770535;