论文标题
几乎是三角数的通用总和，一个例外
Almost universal sums of triangular numbers with one exception
论文作者
论文摘要
对于任意整数$ x $，形式$ t（x）= \ frac {x^2+x} {2} $的整数称为三角形号。对于正整数$α_1，α_2，\ dots，α_k$，$ $δ_{α_1，α_2，\ dots，α_k}（x_1，x_2，x_2，\ dots，dots，x_k）= alian据说数字几乎是普遍的，一个例外，如果二磷剂方程$δ_{α_1，α_2，\ dots，α_k}（x_1，x_1，x_2，\ dots，x_k）= n $具有integer solughter $（x_1，x_2，x_2，x_2，x_2，\ dots，x___k）for z_______ \ k bb bb bb bb bb bb bb bb <k n z \ k. $ n $除了一个。在本文中，我们将所有几乎通用的三角形数字分类，但一个例外。此外，我们提供了几乎普遍性的有效标准，除了任意的三角数量之外，这是Conway，Miller和Schneeberger的“ 15 Theorem”的概括。
For an arbitrary integer $x$, an integer of the form $T(x)=\frac{x^2+x}{2}$ is called a triangular number. For positive integers $α_1,α_2,\dots,α_k$, a sum $Δ_{α_1,α_2,\dots,α_k}(x_1,x_2,\dots,x_k)=α_1 T(x_1)+α_2 T(x_2)+\cdots+α_k T(x_k)$ of triangular numbers is said to be almost universal with one exception if the Diophantine equation $Δ_{α_1,α_2,\dots,α_k}(x_1,x_2,\dots,x_k)=n$ has an integer solution $(x_1,x_2,\dots,x_k)\in\mathbb{Z}^k$ for any nonnegative integer $n$ except a single one. In this article, we classify all almost universal sums of triangular numbers with one exception. Furthermore, we provide an effective criterion on almost universality with one exception of an arbitrary sum of triangular numbers, which is a generalization of "15-theorem" of Conway, Miller and Schneeberger.
