Open AccessSome applications of Brun's criterion
Author(s) -
В. П. Варин
Publication year - 2022
Publication title -
preprint/preprinty ipm im. m.v. keldyša
Language(s) - English
Resource type - Journals
eISSN - 2071-2901
pISSN - 2071-2898
DOI - 10.20948/prepr-2022-14
Subject(s) - mathematics , irrationality , rational number , computer science , arithmetic , discrete mathematics , rationality , epistemology , philosophy
We consider some number-theoretic modifications of algorithms transforming rational sequences. These algorithms are widely applicable in numerical analysis. We use them for construction of the regular continued fractions for some fundamental constants. These algorithms together with the Brun’s criterion allow in a number of cases to establish irrationality of the values algorithmically with the use of only the rational arithmetic.