On a divisibility relation for Lucas sequences

2015/11/06 by Bilu, Yuri, Komatsu, Takao, Luca, Florian +2
#11B39 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1511.01970

Abstract

In this note, we study the divisibility relation U_m| U_n+k^s-U_n^s, where \bf U:=\U_n\_{n≥ 0} is the Lucas sequence of characteristic polynomial x²-ax± 1 and k,m,n,s are positive integers.

Related

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• Primitive Divisors of Lucas Sequences in Polynomial Rings
• On the divisibility of the rank of appearance of a Lucas sequence
• On members of Lucas sequences which are products of Catalan numbers
• Divisors and specializations of Lucas polynomials