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A Note on Partitions into Distinct Parts and Odd Parts

✍ Scribed by Dongsu Kim; Ae Ja Yee

Book ID
110242876
Publisher
Springer US
Year
1999
Tongue
English
Weight
41 KB
Volume
3
Category
Article
ISSN
1382-4090

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πŸ“œ SIMILAR VOLUMES

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Let Q(N ) denote the number of partitions of N into distinct parts. If |(k) := (3k 2 +k)Γ‚2, then it is well known that In this short note we start with Tunnell's work on the ``congruent number problem'' and show that Q(N ) often satisfies ``weighted'' recurrence type relations. For every N there is

Divisibility and Distribution of Partiti
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✍ Jeremy Lovejoy πŸ“‚ Article πŸ“… 2001 πŸ› Elsevier Science 🌐 English βš– 116 KB

We study the generating function for Q(n), the number of partitions of a natural number n into distinct parts. Using the arithmetic properties of Fourier coefficients of integer weight modular forms, we prove several theorems on the divisibility and distribution of Q(n) modulo primes p 5.