More Divisibility Properties for Binomial Coefficients  

作　　者：Jiaqi XIAO Yuqing HE Pingzhi YUAN 

机构地区：[1]School of Mathematics,South China Normal University,Guangdong 510631,P.R.China

出　　处：《Journal of Mathematical Research with Applications》2022年第6期561-579,共19页数学研究及应用（英文版）

基　　金：National Natural Science Foundations of China(Grant No.12171163)。

摘　　要：Let a,b and n be positive integers with a>b,we prove the following divisibility property:For all positive integers n,we have(2bn+1)(2bn+3)(2bn+5)(2bn bn)|15(a-b)(3a-b)(5a-b)(5a-3b)(2an an)(an bn),which extends the result of Yang.And for all positive integers n,we show the following divisibility properties:(6n+1)(4n n)|(12n 6n)(2n n),(12n+1)(5n n)|(15n 3n)(3n-1 n-1),(18n+1)(12n 9n)(8n 2n)|(24n 18n)(4n 2n)(6n 3n).Other more similar divisibility properties are given also.

关 键 词：binomial coefficients p-adic order divisibility property 

分 类 号：O156[理学—数学]