Congruences for sums of binomial coefficients
| dc.creator | Sun, Zhi-Wei | |
| dc.creator | Tauraso, Roberto | |
| dc.date | 2005-02-09 | |
| dc.date | 2007-08-05 | |
| dc.date.accessioned | 2026-07-07T08:22:08Z | |
| dc.date.available | 2026-07-07T08:22:08Z | |
| dc.description | Let q>1 and m>0 be relatively prime integers. We find an explicit period $ν_m(q)$ such that for any integers n>0 and r we have $[n+ν_m(q),r]_m(a)=[n,r]_m(a) (mod q)$ whenever a is an integer with $\gcd(1-(-a)^m,q)=1$, or a=-1 (mod q), or a=1 (mod q) and 2|m, where $[n,r]_m(a)=\sum_{k=r(mod m)}\binom{n}{k}a^k$. This is a further extension of a congruence of Glaisher. | |
| dc.identifier | https://arxiv.org/abs/math/0502187 | |
| dc.identifier | http://arxiv.org/abs/math/0502187 | |
| dc.identifier | J. Number Theory 126(2007), no.2, 287-296 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/135552 | |
| dc.subject | Number Theory | |
| dc.subject | Combinatorics | |
| dc.subject | 11B65, 05A10, 11A07 | |
| dc.title | Congruences for sums of binomial coefficients | |
| dc.type | text |