English

Integer solutions of $a^2+ab+b^2=7^n$

Number Theory 2021-04-20 v1 Combinatorics

Abstract

In this article we will show 22 different proofs for the fact that there exist relatively prime positive integers a,ba,b such that: a2+ab+b2=7na^2+ab+b^2=7^n.

Keywords

Cite

@article{arxiv.2104.08932,
  title  = {Integer solutions of $a^2+ab+b^2=7^n$},
  author = {Tien Nam Le and Tung Tho Nguyen},
  journal= {arXiv preprint arXiv:2104.08932},
  year   = {2021}
}

Comments

This article is written during the REU program at Vietnam National University in 2013. We do not plan to submit it for publication. However, as some other mathematicians recently cited this work, we upload it to Arxiv to make it more official

R2 v1 2026-06-24T01:18:10.326Z