  For an element $a$ of an integral domain D under an equivalence relation
\tau, the \tau-factorization of a is defined as \lambda a_1 a_2... a_k, where
\lambda is a unit in D and a_i \tau a_j for all i, j. An irreducible element
has no proper \tau-factorization; that is, a \tau-factorization in which there
is more than one distinct non-unit factor. In this paper, the irreducible
integers under the congruence modulo n relation for some values of n are found,
and these findings are generalized in the first step toward a general
characterization of the irreducible integers under this relation for any prime
n.
