Perfect Difference Sets: A Residue Class Approach

Rachel Burke Butler University
Faculty Sponsor(s): Ankur Gupta Butler University, Jonathan Webster Butler University
Perfect difference sets are a set of residues, or remainders, under the modulo difference operation. This set, S, contains n elements drawn from V = {0, 1, 2, . . ., v-1}, where v is of the form n^2+ n + 1. All nonzero residues in V can be expressed uniquely in the form x - y (mod v) for x and y in S. Perfect difference sets have been verified to exist when n is a prime power, and the Prime Power Conjecture states that these sets only exist when n is a prime power. The existence of perfect difference sets has been verified for n < 2,000,000,000 by L. Baumert and D. Gordon.

Our previous implementation utilized the tests for perfect difference sets developed by T. Evans and H. Mann. After reorganizing tests according their run time, we eliminated numbers more quickly and verified the Prime Power Conjecture up to n < 1,000,000,000. As this program encountered storage constraints, we cleverly restructured a new program to leverage residue classes.
Mathematics & Computer Science
Oral Presentation

When & Where

11:15 AM
Jordan Hall 238