| Accurate Formulae of $A(n,k)$ and $P(n,k)$ |
| Received:February 28, 2005 Revised:December 13, 2005 |
| Key Words:
Diophantine equation generating function partial fraction.
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| Abstract: |
| Let $A(n,k)$ denote the number of nonnegative integer solutions of Diophantine equation $\sum_{i=1}^kix_i=n$, and $P(n,k)$ denote the number of unordered partitions of an integer $n$ into $k$ parts with each part $\geq 1$. In this paper, accurate formulae of $A(n,k)$ and $P(n,k)$ are established. |
| Citation: |
| DOI:10.3770/j.issn:1000-341X.2007.02.031 |
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