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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2024 MCQ for Mathematics of Computation is 1.78.

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Diophantine equations in partitions
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by Hansraj Gupta PDF
Math. Comp. 42 (1984), 225-229 Request permission

Abstract:

Given positive integers ${r_1},{r_2},{r_3}, \ldots ,{r_j}$ such that \[ {r_1} < {r_2} < {r_3} < \cdots < {r_j} < m;\quad m > 1;\] 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 \[ {r_1}\pmod m,\quad {r_2}\pmod m, \ldots ,{r_j}\pmod m.\] This leads to an identity which is more general though less elegant then the well-known Rogers-Ramanujan identities.
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Additional Information
  • © Copyright 1984 American Mathematical Society
  • 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