二项式系数的James P. Jones问题

On James P .Jones' Problem Concerning Binomial Coefficients

研究了Wolstenholme定理的逆命题,证明：若p∈P,2(?)p,2(?)t,n=prt,且t满足1/2pk＜1/2p(k+1),2(?)k,则(2n-1 n)(?)(mod n3),即此时Wolstenholme定理的逆命题成立.

We studied the inverse proposition of Wolstenholme＇s theorem. It has been proven that： if p∈P,2｜p,2｜t,n=p＇t,and 1/2pk〈t〈1/2p（k＋1）,there 2｜k,then （2n-1/n）≠1（mod n^3）.