On the monotonicity of an additive representation function

摘要

Let .4 = {a1, a2, ... } (a1 < a2 <...) be an infinite sequence of positiveintegers, and let k ≥ 2 be a fixed integer. Let r_1(A,n,k)denote the number of solutionsof a_i_1+ a_i_2++a_i_k=n, a∈A, ... ,a_k∈Fork =2, P. ERDOS, A. SARKOZYand V. T. Sos studied the monotonicity of ri (A, n, k). In this paper I extend one oftheir results to any k > 2.