Let bn be a sequence of real numbers increasing unboundedly, α > 0 and B(n, α) = [bn α]. The conditions on bn are considered, which imply the regularity of distribution of B(n, α) in arithmetic progressions for almost all α > 0. This allows to develop a piece of probabilistic number theory on sequences B(n, α) for almost all α > 0.
This work is licensed under a Creative Commons Attribution 4.0 International License.