2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/71637Recently the author used certain quaternion orders to demonstrate the universality of some quaternary quadratic forms. Here a further study is done on one of these orders analogous to Hurwitz's proof of the formula for the number of representations of a positive integer by sums of four squares using quaternions. The result is the formula for the number of representations of a positive integer by one of the above mentioned quaternary quadratic forms.Approx. 20 pages. Submitted to Journal of Number TheoryNumber Theory11D09; 11D57; 11P05text