关于整数的非负最小剩余与Fermat商的差

On the difference between the non-negative least residue and Fermat quotient of an integer

设p为素数,整数n与p互素。Fermat商qp(n)的定义为qp(n)≡np-1-1/p(mod p),0≤qp(n)≤p-1。此外还规定qp(kp)=0,k∈Z。研究整数n的非负最小剩余rp(n)与Fermat商qp(n)的差的均值分布,并给出了恒等式。

Let p be a prime and let n be arbitrary integer with （n,p） = 1. The Fermat quotient qp（n） is defined as the unique integer with qp（n）=np-1-1/p（mod p）,0≤qp（n）≤p-1.We also define qp （kp）=0 for k∈Z. It is studied that the mean value distribution of the difference between the non-negative least residue rp（n） and Fermat quotient qp（n） of an integer n,and an identity is given.