State University of West Georgia, Charles University, DIMATIA
Abstract
For infinitely many primes p = 4k+1 we give a slightly
improved upper bound for the maximal cardinality of a set B ⊂ Z
p
such that the difference set B−B contains only quadratic residues.
Namely, instead of the ”trivial” bound |B| ≤ √p we prove |B √p | ≤ − 1, under suitable conditions on p. The new bound is valid
for approximately three quarters of the primes p = 4k + 1