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Congruences for sums of binomial coefficients | | Zhi-Wei Sun
; Roberto Tauraso
; | | Date: |
9 Feb 2005 | | Subject: | Number Theory; Combinatorics MSC-class: 11B65; 05A10; 11A07 | math.NT math.CO | | Abstract: | Let m>0 and q>1 be relatively prime integers. We find an explicit period
u_m(q) such that for any integers nge 0 and r we have [n+
u_m(q),r]_m(a)=[n,r]_m(a) (mod q), provided that a=-1 and n
ot=0, or a is an integer with 1-(-a)^m relatively prime to q, where [n,r]_m(a)=sum_{k=r(mod m)}binomial coeff.{n}{k}a^k. This is a further extension of a congruence of Glaisher. | | Source: | arXiv, math.NT/0502187 | | Services: | Forum | Review | PDF | Favorites | |
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