Ryser关于循环Hadamard矩阵的猜想成立的二次剩余和一个新的无穷阶
Quadratic residues and a new infinity of orders for which a conjecture of Ryser about Circulant Hadamard matrices holds
摘要：
对任何正整数$k$，使得$k>1,$存在无穷多个奇整数$h$，它们具有$ω(h) =k$不同的素除子因子，使得不存在$n=4h^2.$阶的循环Hadamard矩阵$H$。此外，我们的主要结果意味着，对所有奇数$h$，对于$1< h < 10^{13}$，不存在$n=4h^2.$阶的循环Hadamard矩阵
英文摘要：
For every positive integer $k$ such that $k>1,$ there are an infinity of odd integers $h$ with $ω(h) =k$ distinct prime divisors such that there do not exist a Circulant Hadamard matrix $H$ of order $n=4h^2.$ Moreover, our main result implies that for all of the odd numbers $h$, with $1< h < 10^{13}$ there is no Circulant Hadamard matrix of order $n=4h^2.$
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
