Mathematics > Number Theory
arXiv:2606.00705 (math)
[Submitted on 30 May 2026]
Abstract:Let $a$, $m$ be positive integers, $1<a<m$, $\gcd(a,m)=1$. We determine the location of a shortest vector in the $2$-dimensional lattices $$ \Lambda(a,m) = \{(x, y)\in\mathbb{Z}\times\mathbb{Z}\mid ax + y\equiv 0~(\bmod\,m)\}. $$ This confirms a conjecture of Han Wu and Guangwu Xu.
Submission history
From: Guixian Zou [view email]
[v1]
Sat, 30 May 2026 12:29:06 UTC (7 KB)
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