On the difference between the non-negative least residue and Fermat quotient of an integer
ZHANG Guotuo, LIU Huaning*
(School of Mathematics, Northwest University, Xi′an 710127, Shaanxi, China)
Abstract:
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-1-1p(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.
KeyWords:
Fermat quotient; non-negative least residue; mean value distribution; identity
