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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: 601

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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: 869 *