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Mathematics of Computation

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Diophantine equations in partitions


Author: Hansraj Gupta
Journal: Math. Comp. 42 (1984), 225-229
MSC: Primary 11P68; Secondary 05A17
DOI: https://doi.org/10.1090/S0025-5718-1984-0725998-2
MathSciNet review: 725998
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Abstract: Given positive integers $ {r_1},{r_2},{r_3}, \ldots ,{r_j}$ such that

$\displaystyle {r_1} < {r_2} < {r_3} < \cdots < {r_j} < m;\quad m > 1;$

we find the number $ P(n,m;R)$ of partitions of a given positive integer n into parts belonging to the set R of residue classes

$\displaystyle {r_1}\pmod m,\quad {r_2}\pmod m, \ldots ,{r_j}\pmod m.$

This leads to an identity which is more general though less elegant then the well-known Rogers-Ramanujan identities.

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DOI: https://doi.org/10.1090/S0025-5718-1984-0725998-2
Article copyright: © Copyright 1984 American Mathematical Society