Difference Set
Let 
be a Group of Order 
and 
be a set of 
elements of . If the set ofdifferences 
contains every Nonzero element of exactly 
times, then is a
-difference set in of Order 
. If 
, thedifference set is called planar. The quadratic residues in the Galois Field 
form a difference set. Ifthere is a difference set of size in a group , then 
must be a multiple of 
, where
is a Binomial Coefficient.
References
Gordon, D. M. ``The Prime Power Conjecture is True for 
.'' Electronic J. Combinatorics 1, R6 1-7, 1994.http://www.combinatorics.org/Volume_1/volume1.html#R6.
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