关于一组同余方程解的概率分布问题

On the Pfobabilistic Distribution Problem of Solutions of a Congruence Equation

主要研究整数ａ，ｂ，ｃ，ｄ满足：ａｂｃｄ≡１（ｍｏｄｎ）且１≤ａ，ｂ，ｃ，ｄ≤ｎ－１时｜ａ＋ｂ－ｃ－ｄ｜的分布性质，即对给定的０＜σ＜２，讨论极限的分布问题，并对某些特殊σ给出一个有趣的概率分布定理。

Let n≥3 be an integer number, for each integer 0<a<n with(n,a)=1, it is clear thatthere exists one and only one a with 0<a<n,so that aa≡1(mod n).The main purpose of this paper isto study the distribution behaviour of|a+b-c-d|(where a,b,c and d satisfies the conditions:1≤a,b,c,d≤n-1,abcd≡1(mod n).That is,given a constant 0<a<2,it is true that the limit ofAn interesting limlt distribution theorem of(* *)for some special σ is given。