Generalized Sidon sets of perfect powers
Sandor Kiss, Csaba Sandor

TL;DR
This paper demonstrates the existence of a dense set of perfect powers with bounded representation counts for sums of h elements, using probabilistic techniques to extend classical additive number theory results.
Contribution
It introduces a probabilistic construction of dense perfect power sets with bounded sum representations, advancing understanding of generalized Sidon sets.
Findings
Existence of dense perfect power sets with bounded sum solutions
Application of probabilistic methods in additive number theory
Extension of Sidon set concepts to perfect powers
Abstract
For and an infinite set of positive integers , let denote the number of solutions of the equation In this paper we prove the existence of a set formed by perfect powers with almost possible maximal density such that is bounded by using probabilistic methods.
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Taxonomy
TopicsAdvanced Topology and Set Theory · Limits and Structures in Graph Theory · Mathematical Dynamics and Fractals
