2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/119359The quantum integer [n]_q is the polynomial 1 + q + q^2 + ... + q^{n-1}, and the sequence of polynomials { [n]_q }_{n=1}^{\infty} is a solution of the functional equation f_{mn}(q) = f_m(q)f_n(q^m). In this paper, semidirect products of semigroups are used to produce families of functional equations that generalize the functional equation for quantum multiplication.7 pagesNumber TheoryQuantum Algebra39B05, 11T22, 30B10, 81R50, 11B13text