Article
Licensed
Unlicensed
Requires Authentication
Infinite Families of Divisibility Properties Modulo 4 for Non-Squashing Partitions into Distinct Parts
-
Published/Copyright:
August 31, 2009
Abstract
In 2005, Sloane and Sellers defined a function b(n) which denotes the number of non-squashing partitions of n into distinct parts. In their 2005 paper, Sloane and Sellers also proved various congruence properties modulo 2 satisfied by b(n). In this note, we extend their results by proving two infinite families of congruence properties modulo 4 for b(n). In particular, we prove that for all k ≥ 3 and all n ≥ 0,
b(22k+1n + 22k–2) ≡ 0 (mod 4) and
b(22k+1n + 3 · 22k–2 + 1) ≡ 0 (mod 4).
Received: 2008-12-15
Accepted: 2009-05-02
Published Online: 2009-08-31
Published in Print: 2009-September
© de Gruyter 2009
You are currently not able to access this content.
You are currently not able to access this content.
Articles in the same Issue
- On Relatively Prime Sets
- Combinatorial Properties of the Antichains of a Garland
- φ(Fn) = Fm
- Twelfth Power Qualified Residue Difference Sets
- On Pebbling Graphs by Their Blocks
- Conjugacy Classes and Class Number
- Infinite Families of Divisibility Properties Modulo 4 for Non-Squashing Partitions into Distinct Parts
- Waring's Number in a Finite Field
- Lucas Diophantine Triples
Articles in the same Issue
- On Relatively Prime Sets
- Combinatorial Properties of the Antichains of a Garland
- φ(Fn) = Fm
- Twelfth Power Qualified Residue Difference Sets
- On Pebbling Graphs by Their Blocks
- Conjugacy Classes and Class Number
- Infinite Families of Divisibility Properties Modulo 4 for Non-Squashing Partitions into Distinct Parts
- Waring's Number in a Finite Field
- Lucas Diophantine Triples
