$$p(5n+4)$$ again
Abstract
Abstract The partition function SOME ( n ) is defined as the sum of all the odd parts in the partitions of n minus the sum of all the even parts in the partitions of n . The generating function for SOME ( n ) is derived, and congruences for SOME ( n ) are found; for instance, $$5 \mid SOME(5n+4)$$ 5 ∣ S O M E ( 5 n + 4 ) . This implies that the sum of all the odd parts in the partitions of $$5n+4$$ 5 n + 4 is divisible by 5, and the same holds for the sum of the even parts.
Fields of Study & Subjects
Advanced Mathematical Identities
Advanced Combinatorial Mathematics
Mathematical functions and polynomials
Publication details
- Journal / source
- The Ramanujan Journal
- Volume
- 69
- Issue
- 1
- Publication date
- 1 January 2026
- Language
- EN