Résumé
A Steinhaus triangle modulo$m$is a finite down-pointing triangle of elements in the finite cyclic group$\mathbb{Z}/m\mathbb{Z}$satisfying the same local rule as the standard Pascal triangle modulo$m$ . A Steinhaus triangle modulo$m$is said to be balanced if it contains all the elements of$\mathbb{Z}/m\mathbb{Z}$with the same multiplicity. In this paper, the existence of infinitely many balanced Steinhaus triangles modulo$m$ , for any positive integer$m$ , is shown. This is achieved by considering periodic triangles generated from interlaced arithmetic progressions. This positively answers a weak version of a problem, due to John C. Molluzzo in 1978, that has remained unsolved to date for the even values of$m\geqslant 12$ .