多重调和级数的几个同余式

Some Congruences Involving Multiple Harmonic Sums

通过研究∑l1+l2+…+ln=p σln/l1…ln-1lkn,σ∈{-1,1}的同余式,当k=2,3时,对任意的正整数n和素数p>n+k-1,得到了∑l1+l2+…+ln=p 1/l1l2…lkn关于模p的同余式.对任意的素数p≥7,证明了∑l1+l2+l3+l4=p (-1)l1/l1l2l3l4关于模的同余式.

Study the conguences for ∑l1＋l2＋…＋ln=p σln/l1…ln-1lkn,σ∈{1,-1},and when k=2,3,for all positive number and prime pn＋k-1,congruences of ∑l1＋l2＋…＋ln=p 1/l1l2…lkn modulo prime p are obtained.For any prime p≥7,congruence of ∑l1＋l2＋l3＋l4=p（-1）l1/l1l2l3l4 modulo prime p is proved.