Prohlížení dle autora "Trojovský, Pavel"

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  • Algebraic numbers as product of powers of transcendental numbers 
    Trojovský, Pavel (MDPI-Molecular diversity preservation international, 2019)
    The elementary symmetric functions played a crucial role in the study of zeros of non-zero polynomials in $C[x]$, and the problem of finding zeros in $Q[x]$ leads to the definition of algebraic and transcendental numbers. ...
  • On characteristic polynomial of higher order generalized Jacobsthal numbers 
    Marques, Diego; Trojovský, Pavel (Springer, 2019)
    In this paper, we study a higher order generalization of the Jacobsthal sequence, namely, the (k,c)}-Jacobsthal sequence (Jn(k,c)) for any integers n, k >= 2. In particular, we find information about roots of its characteristic ...
  • On Diophantine equations involving Lucas sequences 
    Trojovský, Pavel (De Gruyter, 2019)
    In this paper, we study the Diophantine equation $u_n=R(m)P(m)^{Q(m)}$,where $R, P$ and $Q$ are some polynomials (under weak assumptions) and $u_n$ is a Lucas sequence, thus the sequence $(u_n)_{n\geq 0}$ with characteristic ...
  • On Diophantine Equations Related to Order of Appearance in Fibonacci Sequence 
    Trojovský, Pavel (MDPI-Molecular diversity preservation international, 2019)
    Let Fn be the n-th Fibonacci number. Order of appearance z(n) of a natural number n is defined as smallest natural number k, such that n divides Fk. In 1930, Lehmer proved that all solutions of equation z(n)=n+/-1 are prime ...
  • On Terms of Generalized Fibonacci Sequences which are Powers of their Indexes 
    Trojovský, Pavel (MDPI-Molecular diversity preservation international, 2019)
    The k-generalized Fibonacci sequence (Fn(k))n (sometimes also called k-bonacci or k-step Fibonacci sequence), with k >= 2, is defined by the values 0,0, horizontal ellipsis ,0,1 of starting k its terms and such way that ...
  • On the Sum of Reciprocal of Polynomial Applied to Higher Order Recurrences 
    Trojovský, Pavel (MDPI-Molecular diversity preservation international, 2019)
    Recently a lot of papers were devoted to partial infinite reciprocal sums of a higher-order linear recursive sequence. In this paper, we continue this program by finding a sequence which is asymptotically equivalent to ...

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