Glasnik matematički, Vol. 52 No. 1, 2017.
Original scientific paper
https://doi.org/10.3336/gm.52.1.02
A Brocard-Ramanujan-type equation with Lucas and associated Lucas sequences
Istvan Pink
Marton Szikszai
Abstract
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.
Keywords
Brocard-Ramanujan equation; Lucas sequences
Hrčak ID:
183119
URI
Publication date:
21.6.2017.
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