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arXiv · 2111.02746

On a conjecture of Sun involving powers of three

Quan-Hui Yang·Lilu Zhao
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Abstract

Given a positive integer $n\ge 2$, let $D(n)$ denote the smallest positive integer $m$ such that $a^3+a(1\le a\le n)$ are pairwise distinct modulo $m^2$. A conjecture of Z.-W. Sun states that $D(n)=3^k$, where $3^k$ is the least power of $3$ no less than $\sqrt{n}$. The purpose of this paper is to confirm this conjecture.

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Quan-Hui Yang, Lilu Zhao. 2021-11-04. On a conjecture of Sun involving powers of three. https://arxiv.org/abs/2111.02746

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