Some 3-adic congruences for binomial sums  

作　　者：ZHANG Yong PAN Hao 

机构地区：[1]Department of Basic Course,Nanjing Institute of Technology [2]Department of Mathematics,Nanjing University

出　　处：《Science China Mathematics》2014年第4期711-718,共8页中国科学：数学（英文版）

基　　金：supported by National Natural Science Foundation of China (Grant Nos. 11271185,11171140 and 11226277);the Initial Founding of Scientific Research for the Introduction of Talents of Nanjing Institute of Technology,China (Grant No. YKJ201115)

摘　　要：We prove some 3-adic congruences for binomial sums,which were conjectured by Zhi-Wei Sun.For example,for any integer m≡1（mod 3）and any positive integer n,we have v3（1/n ∑n-1X k=0 1/mk 2k/ k〉））≥min{3（n）,3（m-1）-1},where 3（n）denotes the 3-adic order of n.In our proofs,we use several auxiliary combinatorial identities and a series converging to 0 over the 3-adic field.We prove some 3-adic congruences for binomial sums,which were conjectured by Zhi-Wei Sun.For example,for any integer m≡1(mod 3)and any positive integer n,we have31n n.1Xk=01mk 2k k>min{3(n),3(m.1).1},where 3(n)denotes the 3-adic order of n.In our proofs,we use several auxiliary combinatorial identities and a series converging to 0 over the 3-adic field.

关 键 词：3-adic order binomial sum 

分 类 号：O156.1[理学—数学]