论文标题
一套完美的锡顿集
Generalized Sidon sets of perfect powers
论文作者
论文摘要
对于$ h \ ge 2 $和一组无限的正整数$ a $，令$ r_ {a，h}（n）$表示方程$ a_ {1} + a_ {2} + a_ {2} + dots {} + dots {} a_ {1} <a_ {2} <\ dots {} <a_ {h}。$在本文中，我们证明存在由完美幂形成的set $ a $，几乎可能具有最大密度，因此使用概率的方法来界定$ r_ {a，h}（a，h}（a，h}（a，h）$。
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.
