Results 31 to 40 of about 52,567 (260)

An exponential Diophantine equation related to the difference between powers of two consecutive Balancing numbers [PDF]

, 2018
In this paper, we find all solutions of the exponential Diophantine equation $B_{n+1}^x-B_n^x=B_m$ in positive integer variables $(m, n, x)$, where $B_k$ is the $k$-th term of the Balancing sequence.Comment: Comments are ...
Faye, Bernadette, Luca, Florian, Rihane, Salah E., Togbe, Alain   +3 more
core   +2 more sources

A study on the sum of the squares of generalized Balancing numbers: the sum formula $\sum_{k=0}^{n}x^{k}W_{mk+j}^{2}$

Journal of Innovative Applied Mathematics and Computational Sciences, 2021
In this paper, closed forms of the sum formulas $\sum_{k=0}^{n}x^{k}W_{mk+j}^{2}$ for generalized balancing numbers are presented. As special cases, we give sum formulas of balancing, modified Lucas-balancing and Lucas-balancing numbers.
Yüksel Soykan, Erkan Taşdemir, Can Murat Dikmen   +2 more
doaj  

Mersenne-Horadam identities using generating functions

Karpatsʹkì Matematičnì Publìkacìï, 2020
The main object of the present paper is to reveal connections between Mersenne numbers $M_n=2^n-1$ and generalized Fibonacci (i.e., Horadam) numbers $w_n$ defined by a second order linear recurrence $w_n=pw_{n-1}+qw_{n-2}$, $n\geq 2$, with $w_0=a$ and ...
R. Frontczak, T.P. Goy
doaj   +1 more source

Diophantine triples in linear recurrence sequences of Pisot type [PDF]

, 2017
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 the past. The main questions are, as usual, about existence or finiteness
Fuchs, Clemens, Hutle, Christoph, Luca, Florian   +2 more
core   +3 more sources

Balancing and Lucas-balancing Numbers With Real Indices [PDF]

, 2015
In this thesis, we have studied the balancing and Lucas-balancing numbers for real indices. Also we have discussed some properties of balancing numbers with real numbers.
Tanty, Sephali
core   +1 more source

Does Migration Make You Happy?:A Longitudinal Study of Internal Migration and Subjective Well-Being [PDF]

, 2013
The authors acknowledge financial support from the Economic and Social Research Council (ESRC) (RES-625-28-0001). This project is part of the ESRC Centre for Population Change (CPC).
Buck N H, Chiswick B R, Cooke T J, Easterlin R A, Findlay A M, Findlay A M, Florida R, Jacobson L S, Layard R, McCollum A, Schimmack U, van Ham M   +11 more
core   +1 more source

Repdigits as Products of Consecutive Balancing or Lucas-Balancing Numbers

The Fibonacci Quarterly, 2018
Repdigits are natural numbers formed by the repetition of a single digit. In this paper, we explore the presence of repdigits in the product of consecutive balancing or Lucas-balancing numbers.
Rayaguru, Sai Gopal, Panda, Gopal Krishna   +1 more
openaire   +2 more sources

Evaluation of the effectiveness and cost-effectiveness of Families for Health V2 for the treatment of childhood obesity : study protocol for a randomized controlled trial [PDF]

, 2013
Background: Effective programs to help children manage their weight are required. Families for Health focuses on a parenting approach, designed to help parents develop their parenting skills to support lifestyle change within the family.
Griffiths, Frances, Hamborg, Thomas, Khan, Kamran, Kirby, J. (Joanna), Lang, R. (Rebecca), Petrou, Stavros, Poole, Francine, Reddington, Kate, Robertson, Wendy, Rye, G. (Gloria), Simkiss, Douglas E., Stallard, Nigel, Stewart-Brown, Sarah L., Thorogood, Margaret   +13 more
core   +3 more sources

Temporal difference learning with interpolated table value functions [PDF]

, 2009
This paper introduces a novel function approximation architecture especially well suited to temporal difference learning. The architecture is based on using sets of interpolated table look-up functions.
Lucas, Simon M
core   +1 more source

Almost repdigits in balancing and Lucas-balancing sequences [PDF]

Notes on Number Theory and Discrete Mathematics
In this paper, we define the notion of almost repdigit as a positive integer whose digits are all equal except for at most one digit, and we search all terms of the balancing and Lucas-balancing sequences which are almost repdigits.
Manasi K. Sahukar, Hussain Basha
doaj   +1 more source