论文标题
Prime Power Order循环系统决定因素
Prime power order circulant determinants
论文作者
论文摘要
纽曼表明，对于Primes $ p \ geq 5 $，Prime Power Order的积分循环系统$ p^t $无法接受$ p^{t+1} $一旦$ t \ geq 2. $我们显示的许多其他值也被排除在外。特别是，我们表明$ p^{2t} $是任何$ t \ geq 3 $，$ p \ geq 3获得的$ p $的最小功率。前一种情况涉及将$ 1 \ bmod5 $的prime分隔为两组，Tanner's \ textit {perissads}和\ textit {artiad}，后来由E. Lehmer进行了特征。
Newman showed that for primes $p\geq 5$ an integral circulant determinant of prime power order $p^t$ cannot take the value $p^{t+1}$ once $t\geq 2.$ We show that many other values are also excluded. In particular, we show that $p^{2t}$ is the smallest power of $p$ attained for any $t\geq 3$, $p\geq 3.$ We demonstrate the complexity involved by giving a complete description of the $25\times 25$ and $27\times 27$ integral circulant determinants. The former case involves a partition of the primes that are $1\bmod5$ into two sets, Tanner's \textit{perissads} and \textit{artiads}, which were later characterized by E. Lehmer.
