On a question of f-exunits in Z/nZ

摘要

In a commutative ring R with unity, a unit u is called exceptional if u - 1 is also a unit. For R = Z/nZ and for any f(X) is an element of Z[X], an element (u) over bar is an element of Z/nZ is called an "f-exunit" if gcd(f(u), n) = 1. Recently, we obtained the number of representations of a non-zero element of Z/nZ as a sum of two f-exunits for a particular infinite family of polynomials f(X) is an element of Z[X]. In this paper, we complete this problem by proving a similar formula for any non-constant polynomial f(X) is an element of Z[X].