  The purpose of this paper is to introduce basic concepts that are fundamental
in the examination of composite moduli, while avoiding the notoriously
difficult problem of prime-factorization. We introduce a new class of numbers,
called idempotent numbers, that is unavoidable when researching composite
moduli. Among many interesting results, we give generalizations of well-known
theorems and definitions, such as the Euler-Fermat Theorem and the concept of
primitive roots. We consider the generalization of the equivalence condition
for the solvability of a binomial congruence to be the main result of our
paper.
