The Use of Quadratic Residue Research
A quadratic residue search method has previously been suggested
to avoid the clustering usually encountered when hash address collisions
occur and linear search methods are used.  The search size, because
of the property of quadratic residues, is limited to one half of
the storage table.  It is shown that for some classes of prime numbers
the complement of the set of quadratic residues can easily be determined and 
hence the entire table of size p, where p is that prime number, can be searched.
CACM February, 1970
Radke, C. E.
