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On Diophantine, pronic and triangular triples of balancing numbers

Sai Gopal Rayaguru   ORCID icon orcid.org/0000-0003-2575-4768 ; Department of Mathematics, National Institute of Technology Rourkela, Orissa , India
Gopal Krishna Panda ; Department of Mathematics, National Institute of Technology Rourkela, Orissa , India
Alain Togbe ; Department of Mathematics, Statistics and Computer Science, Purdue University Northwest, USA

Puni tekst: engleski, pdf (149 KB) str. 137-155 preuzimanja: 89* citiraj
APA 6th Edition
Rayaguru, S.G., Panda, G.K. i Togbe, A. (2020). On Diophantine, pronic and triangular triples of balancing numbers. Mathematical Communications, 25 (1), 137-155. Preuzeto s https://hrcak.srce.hr/235566
MLA 8th Edition
Rayaguru, Sai Gopal, et al. "On Diophantine, pronic and triangular triples of balancing numbers." Mathematical Communications, vol. 25, br. 1, 2020, str. 137-155. https://hrcak.srce.hr/235566. Citirano 17.04.2021.
Chicago 17th Edition
Rayaguru, Sai Gopal, Gopal Krishna Panda i Alain Togbe. "On Diophantine, pronic and triangular triples of balancing numbers." Mathematical Communications 25, br. 1 (2020): 137-155. https://hrcak.srce.hr/235566
Harvard
Rayaguru, S.G., Panda, G.K., i Togbe, A. (2020). 'On Diophantine, pronic and triangular triples of balancing numbers', Mathematical Communications, 25(1), str. 137-155. Preuzeto s: https://hrcak.srce.hr/235566 (Datum pristupa: 17.04.2021.)
Vancouver
Rayaguru SG, Panda GK, Togbe A. On Diophantine, pronic and triangular triples of balancing numbers. Mathematical Communications [Internet]. 2020 [pristupljeno 17.04.2021.];25(1):137-155. Dostupno na: https://hrcak.srce.hr/235566
IEEE
S.G. Rayaguru, G.K. Panda i A. Togbe, "On Diophantine, pronic and triangular triples of balancing numbers", Mathematical Communications, vol.25, br. 1, str. 137-155, 2020. [Online]. Dostupno na: https://hrcak.srce.hr/235566. [Citirano: 17.04.2021.]

Sažetak
In this paper, we search for some Diophantine triples of balancing numbers. We prove that, if $(6\pm2)B_nB_k+1$ and $(6\pm2)B_{n+2}B_k+1$ are both perfect squares then $k=n+1$, for any positive integer $n \geq 1$. In addition, we define pronic $m$-tuples, triangular $m$-tuples and prove some results related to pronic and triangular triples of balancing numbers.

Ključne riječi
Balancing numbers; Diophantine triples; Linear forms in complex and $p$-adic logarithms

Hrčak ID: 235566

URI
https://hrcak.srce.hr/235566

Posjeta: 176 *