Lehmer DH数与其逆之差的分布性质

On the Distribution Property of Lehmer DH Number

设素数 p≥ 3,对模 p的任一原根 x,且 1≤ x<p,一定存在模 p的唯一的原根 x且 1≤x<p,使得 xx≡ 1(modp) .若 x与 x具有相反的奇偶性 ,则 x就称为 L ehmer DH数 .本文利用广义 Kloosterm ann和估计与三角和估计研究模 p剩余系中 L ehmer DH数与其逆之差的分布 .

Let p≥3 be a prime,for each primitive root x modulo p with 1≤x<p, it is clear that there exists one and only one primitive roor modulo p with 1≤<p such that x≡1( mod p) .The number x is called as Lehmer DH mumber if x and are of opposite parity This paper is to study the distribution property of Lehmer DH number by using the estimation of general Kloostermann sum and trigonometric sum