University of Ostrava

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20022026

most citedImaging linear and circular polarization features in leaves with complete Mueller matrix polarimetry

59 citations

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10 papers · 1 filter

math.NT2018★ 8 cited

One-sided Diophantine approximations

Jaroslav Hančl, Ondřej Turek

The paper deals with best one--sided (lower or upper) Diophantine approximations of the $ℓ$ -th kind ( $ℓ \in N$ ). We use the ordinary continued fraction expansions to f…

math.NT2018★ 13 cited

On certain sums concerning the gcd's and lcm's of $k$ positive integers

Titus Hilberdink, Florian Luca, László Tóth

We use elementary arguments to prove results on the order of magnitude of certain sums concerning the gcd's and lcm's of $k$ positive integers, where $k \geq 2$ is fixed. We refine a…

math.NT2017★ 3 cited

Diophantine triples in linear recurrence sequences of Pisot type

Clemens Fuchs, Christoph Hutle, Florian Luca

The study of Diophantine triples taking values in linear recurrence sequences is a variant of a problem going back to Diophantus of Alexandria which has been studied quite a lot in…

math.NT2017★ 2 cited

Constrained ternary integers

Florian Luca, Pieter Moree, Robert Osburn +2

An integer $n$ is said to be ternary if it is composed of three distinct odd primes. In this paper, we asymptotically count the number of ternary integers $n \leq x$ with the const…

math.NT2017★ 1 cited

A variation on the theme of Nicomachus

Florian Luca, Geremías Polanco, Wadim Zudilin

We prove some conjectures of K. Stolarsky concerning the first and third moment of the Beatty sequences with the golden section and its square.

math.NT2017★ 19 cited

On a problem of Pillai with $k$ -generalised Fibonacci numbers and powers of $2$

Mahadi Ddamulira, Carlos A. Gómez, Florian Luca

For an integer $k \geq 2$ , let ${F_{n}^{(k)}}_{n \geq 0}$ be the $k$ --generalized Fibonacci sequence which starts with $0, \dots, 0, 1$ ( $k$ terms) and each term afterwar…