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THE NUMBER OF PARTITIONS INTO DISTINCT PARTS MODULO POWERS OF 5

Published online by Cambridge University Press:  24 March 2003

JEREMY LOVEJOY
JEREMY LOVEJOY
Affiliation:
Projet ‘Theorie des Nombres’, Institut de Mathematiques de Jussieu, Case 247, 4 Place Jussieu, 75252 Paris, CEDEX 05 Francelovejoy@math.jussieu.fr
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Abstract

A relationship is established between the factorization of $24 n + 1$ and the 5-divisibility of $Q(n)$ , where $Q(n)$ is the number of partitions of $n$ into distinct parts. As an application, an abundance of infinite families of congruences for $Q(n)$ modulo powers of 5 are explicitly exhibited.

Type
NOTES AND PAPERS
Information
Bulletin of the London Mathematical Society , Volume 35 , Issue 1 , January 2003 , pp. 41 - 46
Copyright
© The London Mathematical Society 2003

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Footnotes

The author thanks the NSF for its generous support.