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arXiv · 1711.00186

On additive representation functions

Yong-Gao Chen·Hui Lv
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Abstract

Let $A$ be an infinite set of natural numbers. For $n\in \mathbb{N}$, let $r(A, n)$ denote the number of solutions of the equation $n=a+b$ with $a, b\in A, a\le b$. Let $|A(x)|$ be the number of integers in $A$ which are less than or equal to $x$. In this paper, we prove that, if $r(A, n)\not= 1$ for all sufficiently large integers $n$, then $|A(x)|> \frac 12 (\log x/\log\log x)^2$ for all sufficiently large $x$.

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Yong-Gao Chen, Hui Lv. 2017-11-01. On additive representation functions. https://doi.org/10.5486/pmd.2018.8175

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