Fix a positive integer and a finite set whose elements are in arithmetic progression. We give a formula for the number of nonempty subsets of this set that are coprime to the given integer. A similar formula is given when we restrict our attention to the subsets having the same fixed cardinality. These formulas generalize previous results of El Bachraoui.
Let A be a finite union of disjoint sets of consecutive integers and let n be a positive integer. We give a formula for the number of relatively prime subsets (resp., 1 relatively prime subsets of cardinality k) of A, which generalizes results of Nathanson, El Bachraoui and others. We give as well similar formulas for the number of subsets with gcd coprime… (More)
Let f := p/q ∈ K(x) be a rational function in one variable. By Lüroth's theorem, the collection of intermediate fields K(f) L K(x) is in bijection with inequivalent proper decompositions f = g • h, with g, h ∈ K(x) of degrees ≥ 2. In (Alonso, Gutierrez & Recio 1995) an algorithm is presented to calculate such a function decomposition. In this paper we… (More)
This work was designated to monitor the coagulation abnormalities associated with the gradual progression of liver diseases. The study included fifty patients; forty were diagnosed with liver cirrhosis with different stages categorized according to the Childs-Pugh classification and another ten patients were diagnosed with hepatocellular carcinoma (HCC).… (More)