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- Title
Arithmetic properties for Fu's 9 dots bracelet partitions.
- Authors
Yao, Olivia X. M.
- Abstract
The notion of Fu's k dots bracelet partitions was introduced by Shishuo Fu. For any positive integer k, let 픅k(n) denote the number of Fu's k dots bracelet partitions of n. Fu also proved several congruences modulo primes and modulo powers of 2. Recently, Radu and Sellers extended the set of congruences proven by Fu by proving three congruences modulo squares of primes for 픅5(n), 픅7(n) and 픅11(n). More recently, Cui and Gu, and Xia and the author derived a number of congruences modulo powers of 2 for 픅5(n). In this paper, we prove four congruences modulo 2 and two congruences modulo 4 for 픅9(n) by establishing the generating functions of 픅9(An+B) modulo 4 for some values of A and B.
- Subjects
ARITHMETIC functions; PARTITIONS (Mathematics); PRIME numbers; GEOMETRIC congruences; MATHEMATICAL analysis
- Publication
International Journal of Number Theory, 2015, Vol 11, Issue 4, p1063
- ISSN
1793-0421
- Publication type
Article
- DOI
10.1142/S1793042115500566