Published online by Cambridge University Press: 17 April 2009
Let A = {a1, a2,…}(a1 < a2 < …) be an infinite sequence of positive integers. Let k ≥ 2 be a fixed integer and denote by Rk(n) the number of solutions of . Erdős, Sárközy and Sós studied the boundness of |R2(n + 1) − R2(n)| and the monotonicity property of R2(n). In this paper, we extend some results to k > 2.