2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/169563We examine statistical properties of the Calkin--Wilf tree and give number-theoretical applications.19 pages (preprint). Some results of this paper are already well-known, some (p-adic distribution and properties of the moments) are new and will be merged into paper arXiv:0801.0051Number Theory11A55, 26A30text