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Congruences for sums of binomial coefficients  ZhiWei Sun
; Roberto Tauraso
;  Date: 
9 Feb 2005  Subject:  Number Theory; Combinatorics MSCclass: 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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