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https://doi.org/10.3336/gm.52.1.02

A Brocard-Ramanujan-type equation with Lucas and associated Lucas sequences

Istvan Pink
Marton Szikszai

Puni tekst: engleski, pdf (140 KB) str. 11-21 preuzimanja: 388* citiraj
APA 6th Edition
Pink, I. i Szikszai, M. (2017). A Brocard-Ramanujan-type equation with Lucas and associated Lucas sequences. Glasnik matematički, 52 (1), 11-21. https://doi.org/10.3336/gm.52.1.02
MLA 8th Edition
Pink, Istvan i Marton Szikszai. "A Brocard-Ramanujan-type equation with Lucas and associated Lucas sequences." Glasnik matematički, vol. 52, br. 1, 2017, str. 11-21. https://doi.org/10.3336/gm.52.1.02. Citirano 27.09.2020.
Chicago 17th Edition
Pink, Istvan i Marton Szikszai. "A Brocard-Ramanujan-type equation with Lucas and associated Lucas sequences." Glasnik matematički 52, br. 1 (2017): 11-21. https://doi.org/10.3336/gm.52.1.02
Harvard
Pink, I., i Szikszai, M. (2017). 'A Brocard-Ramanujan-type equation with Lucas and associated Lucas sequences', Glasnik matematički, 52(1), str. 11-21. https://doi.org/10.3336/gm.52.1.02
Vancouver
Pink I, Szikszai M. A Brocard-Ramanujan-type equation with Lucas and associated Lucas sequences. Glasnik matematički [Internet]. 2017 [pristupljeno 27.09.2020.];52(1):11-21. https://doi.org/10.3336/gm.52.1.02
IEEE
I. Pink i M. Szikszai, "A Brocard-Ramanujan-type equation with Lucas and associated Lucas sequences", Glasnik matematički, vol.52, br. 1, str. 11-21, 2017. [Online]. https://doi.org/10.3336/gm.52.1.02

Sažetak
This paper deals with a Brocard-Ramanujan-type equation of the form
un1un2 ⋯ unk+1=um2
in unknown nonnegative integers k,n1,n2, …,nk and m with k≥ 1, where u=(un)n=0∞ is either a Lucas sequence or its associated sequence. For certain infinite families of sequences we completely solve the above equation, extending some results of Marques [15], Szalay [21] and Pongsriiam [18]. The ingredients of the proofs are factorization properties of Lucas sequences, the celebrated result of Bilu, Hanrot and Voutier on primitive divisors of Lucas sequences and elementary estimations concerning the terms involved.

Ključne riječi
Brocard-Ramanujan equation; Lucas sequences

Hrčak ID: 183119

URI
https://hrcak.srce.hr/183119

Posjeta: 517 *