Representations of integers as the sum of k terms
Paul L. Erdos, Prasad Tetali · Random Structures and Algorithms · 1990
Abstract A set of natural numbers is called an asymptotic basis of order k if every number (sufficiently large) can be expressed as a sum of k distinct numbers from the set. in this paper we prove that, for every fixed k, there exists an asymptotic basis of order k such that the number of representations of n is Θ(log n).