代数方法下的伪原根个数统计算法

Algebra Method in Calculating Pseudo-Primitive Roots

为了求Zn*中伪原根个数,应用有限Abel群的直和分解理论,对有限Abel群Zn*的不同次数元素的个数进行统计.给出Zn*中伪原根数的3种不同计算方法,并且解决了Jacques Dubrois和Jean-Guillaume Dumas提出的猜想:n为奇数,Zn*中伪原根个数g(n)≥((n)).

Through direct sum factoring in finite able group,the number of elements with different order in is calculated.There are three different ways introduced to calculate the number of pseudo-primitive root in.Finally,corollary is put forward to solve the conjecture which is declared by Jacques Dubrois and Jean-Guillaume Dumas.