This book presents state-of-the-art research on the distribution modulo one of sequences of
integral powers of real numbers and related topics. Most of the results have never before …

Fibonacci numbers which are concatenations of two repdigits Page 1 Quaestiones
Mathematicae 2021, 44(2): 281–290 c⃝ 2019 NISC (Pty) Ltd https://doi.org/10.2989/16073606.2019.1686439 …

In this paper, we find all the solutions of the title Diophantine equation in positive integer
variables (n, m, a), where F k is the k th term of the Fibonacci sequence. The proof of our …

Repdigits as sums of three Fibonacci numbers 1. The main result and its proof Page 1
MATHEMATICAL COMMUNICATIONS 1 Math. Commun. 17(2012), 1–11 Repdigits as …

Furstenberg has conjectured that the only continuous probability measure on the circle T=
R/Z which is invariant under both x↦ 2 x and x↦ 3 x is Lebesgue measure. We shall show …

We find all positive integer solutions of the Diophantine equation F n+ F m+ F e= 2 a, where
F k is the k th term of the Fibonacci sequence. This paper continues and extends the …

We prove that if q≥ 5 is an integer, then every qth power of an integer contains at least 5
nonzero digits in its binary expansion. This is a particular instance of one of a collection of …

Given positive integers A1,∙∙∙, At and b≥ 2, we write A1∙∙∙ At (b) for the integer whose base-b
representation is the concatenation of the base-b representations of A1,∙∙∙, At. In this paper …

Let (un) n be a linear recurrence sequence of integers and let b> 1 be a natural number. In
this paper, we show that under some mild technical assumptions the base b expansion of …

We encounter integer numbers daily, and they are literally everywhere around us. It is not
possible to avoid them, ignore them, or to be indifferent to them. So let us take together a …