On the Distribution of Inverses Modulon

Abstract Let n >2 be an integer, and for each integer 0 a n with ( a ,  n )=1, define ā by the congruence aā ≡1 (mod  n ) and 0 ā n . The main purpose of this paper is to study the distribution behaviour of | a − ā |,[formula]where φ ( n ) is the Euler function, and #{…} denotes the number of elements of the set {…}.