A Brocard-Ramanujan-type equation with Lucas and associated Lucas sequences
| Autor: | Márton Szikszai, István Pink |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2017 |
| Předmět: |
Lucas sequence
General Mathematics Brocard 010102 general mathematics Mathematical analysis 010103 numerical & computational mathematics 01 natural sciences Brocard-Ramanujan equation Lucas sequences Ramanujan's sum Combinatorics Type equation symbols.namesake Lucas number symbols 0101 mathematics Mathematics |
| Zdroj: | Glasnik matematički Volume 52 Issue 1 |
| ISSN: | 1846-7989 0017-095X |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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