On a Conjecture of Sun Zhi-Wei and Related Diophantine Equations

Wang Jia-Hui; Zhu Hui-Lin

On a Conjecture of Sun Zhi-Wei and Related Diophantine Equations

Number Theory 2022-02-18 v1

Authors: Wang Jia-Hui , Zhu Hui-Lin

Abstract

For any integer $m\ge0$ , we recall that triangular numbers are those $\mathbf{T}(m)=\frac{m(m+1)}{2}$ . A conjecture of Sun Zhi-Wei states that an integer $2^n\pm n$ with any $n>2$ can not be a triangular number. The motivation of this work is to confirm this conjecture.

Keywords

triangular numbers diophantine equations sun zhi-wei conjecture exponential sums

Cite

@article{arxiv.2202.08738,
  title  = {On a Conjecture of Sun Zhi-Wei and Related Diophantine Equations},
  author = {Wang Jia-Hui and Zhu Hui-Lin},
  journal= {arXiv preprint arXiv:2202.08738},
  year   = {2022}
}

Related papers

View all related →