Let be a Group of Order and be a set of elements of . If the set of differences contains every Nonzero element of exactly times, then is a -difference set in of Order . If , the difference set is called planar. The quadratic residues in the Galois Field form a difference set. If there is a difference set of size in a group , then must be a multiple of , where is a Binomial Coefficient.
See also Bruck-Ryser-Chowla Theorem, First Multiplier Theorem, Prime Power Conjecture
Gordon, D. M. ``The Prime Power Conjecture is True for .'' Electronic J. Combinatorics 1, R6 1-7, 1994.