论文标题
Sylvester在算术进展中设置的Frobenius汇总的汇总和初始差距
Sylvester sums on the Frobenius set in arithmetic progression with initial gaps
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 $的某些公式可能存在，包括那些形成算术进度及其修改的公式。在本文中，我们为非代表性正整数（Sylvester Sum）的总和提供了明确的公式，以及Frobenius数字以及$ a_1，a_1，a_2，\ dots，a_k dots，a_k $ a_k $与初始差距形成arithmetic进程的非代表性正整数（sylverser编号）的数量。
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 explicit formulae for the sum of nonrepresentable positive integers (Sylvester sum) as well as Frobenius numbers and the number of nonrepresentable positive integers (Sylverster number) for $a_1,a_2,\dots,a_k$ forming arithmetic progressions with initial gaps.
