Solutions to Two Problems of Sárközy and Sós on Additive Representation Functions

Peiru Kuang, Yan Wang

For a set $A\subseteq {\mathbb{N}}_0$, let $r_1(A,n)$ denote the number of solutions of the equation $a+a^{\prime }=n$ with $a,a^{\prime }\in A$, and let $r_2(A,n)$ denote the number of…