Abstract
In this note, we shall give conditions which guarantee that 1-qb1-qa[nm]∈Z[q] holds. We shall provide a full characterisation for 1-qb1-qa[kam]∈Z[q]. This unifies a variety of results already known in literature. We shall prove new divisibility properties for the binomial coefficients and a new divisibility result for a certain finite sum involving the roots of the unity.
Original language | English |
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Pages (from-to) | 291-298 |
Number of pages | 8 |
Journal | Ramanujan Journal |
Volume | 45 |
Issue number | 1 |
DOIs | |
Publication status | Published - Jan 1 2018 |
Keywords
- Binomial coefficients
- Divisibility
- q-Binomial coefficients
ASJC Scopus subject areas
- Algebra and Number Theory