Congruences for sums of binomial coefficients

dc.creatorSun, Zhi-Wei
dc.creatorTauraso, Roberto
dc.date2005-02-09
dc.date2007-08-05
dc.date.accessioned2026-07-07T08:22:08Z
dc.date.available2026-07-07T08:22:08Z
dc.descriptionLet 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.identifierhttps://arxiv.org/abs/math/0502187
dc.identifierhttp://arxiv.org/abs/math/0502187
dc.identifierJ. Number Theory 126(2007), no.2, 287-296
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/135552
dc.subjectNumber Theory
dc.subjectCombinatorics
dc.subject11B65, 05A10, 11A07
dc.titleCongruences for sums of binomial coefficients
dc.typetext

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