On inversion in ℤ2n-1

In this paper we determined explicitly the multiplicative inverses of the Dobbertin and Welch APN exponents in Z"2"^"n"-"1, and we described the binary weights of the inverses of the Gold and Kasami exponents. We studied the function Inv"d(n), which for a fixed positive integer d maps integers n>=1 to the least positive residue of the inverse of d modulo 2^n-1, if it exists. In particular, we showed that the function Inv"d is completely determined by its values for 1=