论文标题
紧密的通用八角形形式
Tight universal octagonal forms
论文作者
论文摘要
令$ p_8（x）= 3x^2-2x $。对于正整数，$ a_1，a_2，\ dots，a_k $，$ a_1p_8（x_1）+a_2p_8（x_2）+\ cdots+cdots+a_kp_8（x_k）$的多项式称为八角形式。对于一个正整数$ n $，如果代表（超过$ \ mathbb {z} $），八角形式称为紧密$ \ mathcal t（n）$ - 通用形式，每个正整数大于或等于$ n $，并且不会代表任何积极的integer，则没有任何较小的$ n $。在本文中，我们找到了每$ n \ ge 2 $的所有紧密$ \ mathcal t（n）$ - 通用八角形式。此外，我们提供了有关杂物八角形式的紧密$ \ Mathcal t（n）$的有效标准，这是Conway和Schneeberger的“ 15 Theorem”的概括。
Let $P_8(x)=3x^2-2x$. For positive integers $a_1,a_2,\dots,a_k$, a polynomial of the form $a_1P_8(x_1)+a_2P_8(x_2)+\cdots+a_kP_8(x_k)$ is called an octagonal form. For a positive integer $n$, an octagonal form is called tight $\mathcal T(n)$-universal if it represents (over $\mathbb{z}$) every positive integer greater than or equal to $n$ and does not represent any positive integer less than $n$. In this article, we find all tight $\mathcal T(n)$-universal octagonal forms for every $n\ge 2$. Furthermore, we provide an effective criterion on tight $\mathcal T(n)$-universality of an arbirary octagonal form, which is a generalization of "15-Theorem" of Conway and Schneeberger.
