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arXiv · 2201.10727

On a conjecture of Erd\H{o}s

Yong-Gao Chen·Yuchen Ding
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Abstract

Let $\mathcal{P}$ denote the set of all primes. In 1950, P. Erd\H{o}s conjectured that if $c$ is an arbitrarily given constant, $x$ is sufficiently large and $a_1,\dots , a_t$ are positive integers with $a_1 \log x$, then there exists an integer $n$ so that the number of solutions of $n=p+a_i$ $(p\in \mathcal{P}, 1\le i\le t)$ is greater than $c$. In this note, we confirm this old conjecture of Erd\H{o}s.

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Yong-Gao Chen, Yuchen Ding. 2022-01-26. On a conjecture of Erd\H{o}s. https://arxiv.org/abs/2201.10727

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