On the decomposition of modular multiplicative inverse operators via a new functional algorithm approach to Bachet's-Bezout's Lemma

摘要

In this paper, we consider modular multiplicative inverse operators (MMIO)'s of the form: J(m+n):(Z/(m+n)Z)~*→Z/(m+n)Z,J(m+n)(a)=a-1. A general method to decompose J_(m+n)(·) over group of units (Z/(m + n)Z)~* is derived. As result, an interesting decomposition law for these operators over (Z/(m + n)Z)~* is established. Numerical examples illustring the new results are given. This, complement some recent results obtained by the author for (MMIO)'s defined over group of units of the form (Z/QZ)~* with Q = m × n > 2.