2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/169993The Lagrange theorem on continued fractions states that a number is a quadratic surd if and only if its continued fraction expansion is eventually periodic. The current paper is devoted to a multidimensional generalization of this fact. As a multidimensional analog of continued fractions so called Klein polyhedra are considered: given an irrational lattice in an n-dimensional Euclidean space, its Klein polyhedron is defined as the convex hull of nonzero lattice points with nonnegative coordinates.13 pages, 15 referencesNumber Theory11H06, 11H46, 11H50text