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

TL;DR

This paper investigates Sun Zhi-Wei's conjecture that for any integer n>2, the numbers 2^n ± n are not triangular numbers, aiming to confirm this conjecture through mathematical analysis.

Contribution

The paper provides a proof or significant evidence supporting Sun Zhi-Wei's conjecture regarding the non-triangularity of 2^n ± n for n>2.

Findings

Confirmed that 2^n ± n are not triangular numbers for n>2

Established new bounds or properties related to the conjecture

Contributed to the understanding of the structure of related Diophantine equations

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.