The transcendental \(p-\) adic numbers are divided into the three disjoint classes S, T, U and the class U is subdivided into the subclasses \(U_{m}\) \((m=1,2,3,\ldots )\) with respect to Mahler’s classification. Using Ruban continued fraction expansions of \(p-\) adic Liouville numbers, we prove that integral combinations with algebraic \(p-\) adic number coefficients of certain \(p-\) adic Liouville numbers are Mahler’s \(p-\) adic \(U_{m}-\) numbers, where m is the degree of the \(p-\) adic algebraic number field determined by these algebraic \(p-\) adic number coefficients, and we construct explicit examples to illustrate our results.
