2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/121233A decomposition of a natural number n is a sequence of consecutive natural numbers that sums to n. We construct a one-to-one correspondence between the odd factors of a natural number and its decompositions. We study the decompositions by their lengths and introduce the concept of length spectrum. Also, we use diagrams to illustrate the ideas behind our proofs.7 pages, 1 table, 3 figures. To appear in the College Journal of Mathematics, March 2007History and OverviewNumber Theory01A99; 11A99text