Abstract For $$h \ge 2$$ h ≥ 2 and an infinite set of positive integers A , let $$R_{A,h}(n)$$ R A , ( n ) denote the number rep...

A set A of positive integers is a perfect difference set if every nonzero integer has an unique representation as the difference of two elements of A. We construct dense perfect difference sets from dense Sidon sets. As a consequence of this new approach we prove that there exists a perfect difference set A such that A(x) ≫ x √ . Also we prove that there exists a perfect difference set A such t...