Lehmer D H数与它的逆之差的分布

Distribution of Difference Between Lehmer D H Number and Its Inverse

设n≥ 3为存在原根的整数 ,对任意整数 1≤a <n且 (a ,n) =1,显然存在唯一的整数 1≤ a <n ,使得a a≡ 1(modn) .如果a与 a具有相反的奇偶性 ,定义数a为LehmerDH数 .本文利用了广义Kloostermann和估计研究了LehmerDH数与它的逆之差的分布性质 。

Let n≥3 be an odd number and contain a primitive root,for each 1≤a<n with (a,n)=1, It is clear that there exists one and only one 1≤<n such that a≡ 1(mod n ). Such number a is called as lehmer D H number if a and are of opposite parity. This paper is to study the distribution property of difference between lehmer D H number and its inverse by use the estimation of kloosterman’s sum. and given an asymptotic formula.