2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/33281A generalization of numeration system in which the set N of the natural numbers is recognizable by finite automata can be obtained by describing a lexicographically ordered infinite regular language. Here we show that if P belonging to Q[x] is a polynomial such that P(N) is a subset of N then we can construct a numeration system in which the set of representations of P(N) is regular. The main issue in this construction is to setup a regular language with a density function equals to P(n+1)-P(n) for n large enough.11 pagesComputational ComplexityF.1.1; F.4.3text