Article
Ramanujan's Three Famous Partition Congruences
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Abstract
Let $p(n)$ denote the number of partitions of $n$ where $n$ is a positive integer. In this paper, we study Ramanujan's congruences for the Partition function $p(n)$, especially $p(5n+4)$, $p(7n+5)$ and $p(11n+6) \equiv 0 \pmod{5,7,11}$ respectively and explore the different types of partition congruences along with proof of some partition congruences.
Keywords
Ramanujan, Partitions, Congruences, Pentagonal Number Theorem, Eisenstein series
Citation
Konch, A. (2020). Ramanujan's three famous partition congruences. Turkish Journal of Computer and Mathematics Education, 11(1), 759–767.
A. Konch, “Ramanujan's three famous partition congruences,” Turkish Journal of Computer and Mathematics Education, vol. 11, no. 1, pp. 759–767, 2020.
Konch A. Ramanujan's three famous partition congruences. Turkish Journal of Computer and Mathematics Education. 2020;11(1):759–767.
Konch, A. (2020), ‘Ramanujan's three famous partition congruences’, Turkish Journal of Computer and Mathematics Education, 11(1), pp. 759–767.
Konch, Abhijit. “Ramanujan's Three Famous Partition Congruences.” Turkish Journal of Computer and Mathematics Education, vol. 11, no. 1, 2020, pp. 759–767.
Konch, Abhijit. “Ramanujan's Three Famous Partition Congruences.” Turkish Journal of Computer and Mathematics Education 11, no. 1 (2020): 759–767.
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Published by: Engineering Journals
