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arXiv · 2006.02783

Generalized Sidon sets of perfect powers

Sandor Kiss·Csaba Sandor
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Abstract

For $h \ge 2$ 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.

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Sandor Kiss, Csaba Sandor. 2020-06-04. Generalized Sidon sets of perfect powers. https://arxiv.org/abs/2006.02783

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