Generalized Sidon sets of perfect powers

Sandor Kiss; Csaba Sandor

paper

Generalized Sidon sets of perfect powers

arXiv:2006.02783

Abstract

For $h \geq 2$ and an infinite set of positive integers $A$ , let $R_{A, h} (n)$ denote the number of solutions of the equation $a_{1} + a_{2} + \dots + a_{h} = n, a_{1} \in A, \dots, a_{h} \in A, a_{1} < a_{2} < \dots < a_{h} .$ In this paper we prove the existence of a set $A$ formed by perfect powers with almost possible maximal density such that $R_{A, h} (n)$ is bounded by using probabilistic methods.