二项式序列b_n(r,s)在模p下的同余性质

Congruence Properties of Binomialarray b_n (r,s) in Module p

将序列bn(r)=∑nk=1nkink-1r-i推广成bn(r,s)=∑nk=1nkrnk-1s,并研究序列bn(r,s)在modp下的同余性质,得出对任意奇素数p和k,r,s∈N,有bkp(r,s)≡0(modp)的结论.

The binomial array bn（r）=^n∑k=1（nk）^i（nk-1）^r-i is extended to bn（r,s）=^n∑k=1（nk）^r（nk-1）^s and the congruence properties of binomial array bn（r,s） in module p is studied.The result that bkp（r,s）≡0（mod p） is true for every odd prime number p and k,r,s∈N is obtained.