论文标题
Sylvester Power and frobenius的加权总和算术进展
Sylvester power and weighted sums on the Frobenius set in arithmetic progression
论文作者
论文摘要
令$ a_1，a_2，\ dots，a_k $为正整数，$ \ gcd（a_1，a_2，\ dots，a_k）= 1 $。 Frobenius编号是最大的正整数，不可用$ a_1，a_2，\ dots，a_k $表示。当$ k \ ge 3 $时，通常没有明确的公式，但是特殊序列$ a_1，a_2，\ dots，a_k $的某些公式可能存在，包括那些形成算术进度及其修改的公式。在本文中，我们为非代表性积极整数的功率和加权总和提供了公式。作为应用程序，我们显示了$ a_1，a_2，\ dots，a_k $形成算术进度的这些总和的明确表达式。
Let $a_1,a_2,\dots,a_k$ be positive integers with $\gcd(a_1,a_2,\dots,a_k)=1$. Frobenius number is the largest positive integer that is NOT representable in terms of $a_1,a_2,\dots,a_k$. When $k\ge 3$, there is no explicit formula in general, but some formulae may exist for special sequences $a_1,a_2,\dots,a_k$, including, those forming arithmetic progressions and their modifications. In this paper, we give formulae for the power and weighted sum of nonrepresentable positive integers. As applications, we show explicit expressions of these sums for $a_1,a_2,\dots,a_k$ forming arithmetic progressions.
