Mathematics Commons^™

Maximal Residue Difference Sets Modulo P, Duncan A. Buell, Kenneth S. Williams

Faculty Publications

Let p ≡ 1 (mod 4) be a prime. A residue difference set modulo p is a set S = {a_i} of integers a_i such that (a_i/p) = +1 and ((a_i - a_j)/p) = +1 for all i and j with i ≠ j, where (n/p) is the Legendre symbol modulo p. Let m_p be the cardinality of a maximal such set S. The authors estimate the size of m_p.