Well Distribution of Sidon Sets in Residue Classes

A setAof non-negative integers is aSidon setif the sumsa+b(a, b A, a b) are distinct. Assume thata [1, n] and that A=(1+o(1))n1/2. Letm 2 be an integer. In Theorem 1 I prove that asymptotically 1/mof all elements inAfall into each residue class modulom. Whenm=2 I prove a sharper result in Theorem 2. Assume that A n1/2. Then the difference between the number of odd and the number of even elements inAisO(n3/8). If the interval [1, n] is divided intomequal parts and the number of elements fromAin each part is counted, then similar results hold for these counts.