关于同余式sum from i=1 to k(x_i^2≡0(mod p))(1≤x_1<x_2<…<x_k≤(P-1)/2)的解数公式

ON THE NUMBER OF SOLUTIONS OF THE CONGRUENCE sum from i=1 to k(x_i^2≡0(mod p))(1≤x_1<x_2<…<x_k≤(P-1)/2)

最近,Takashi Agoh对于素数p≡1(mod4)给出了计算二次域Q(p^(1/2))的类数h的一个公式,此公式仅依赖于Q(p^(1/2))的基本单位ε,素数p以及数a=1+sum from k=1 to(p-1)/2((-1)~kN_K).孙琦教授对奇素数p,得到N_k的若干性质和计算N_2,N_3,N_4的公式.本文对奇素数p,得到N_k的若干新性质和N_5,N_6的计算公式,

Let p be an odd prime with p=1(mod 4) and the fundamental unit of real quadratic field Q over the rationals Q. Also let h be the classnumber of Q (p) . Recently, Takashi Agoh proves that h=log+ap}-log(p-1)/log ε where a=1(-1)kNk, and Nk the number ofsolutions of the congruence. And Sun Qi obtains some properties of Nk and formulae computing N2, N3, N4, where p is a odd prime.In this paper, we obtain some new properties of Nk and formulae computing N5, N6. where p is a odd prime.