On members of Lucas sequences which are products of factorials

Authors

Shanta Laishram, Indian Statistical Institute (Delhi Centre)
Florian Luca, University of the Witwatersrand, Johannesburg
Mark Sias, University of Johannesburg

Article Type

Research Article

Publication Title

Monatshefte fur Mathematik

Abstract

We show that if {Un}n≥0 is a Lucas sequence, then the largest n such that | Un| = m1! m2! ⋯ mk! with 1 ≤ m1≤ m2≤ ⋯ ≤ mk satisfies n< 62,000. When the roots of the Lucas sequence are real, we have n∈ { 1 , 2 , 3 , 4 , 6 , 12 }. As a consequence, we show that if {Xn}n≥1 is the sequence of X-coordinates of a Pell equation X2- dY2= ± 1 with a non-zero integer d> 1 , then Xn= m! implies n= 1.

First Page

329

Last Page

359

DOI

10.1007/s00605-020-01455-y

Publication Date

10-1-2020

Comments

Open Access, Green

Recommended Citation

Laishram, Shanta; Luca, Florian; and Sias, Mark, "On members of Lucas sequences which are products of factorials" (2020). Journal Articles. 122.
https://digitalcommons.isical.ac.in/journal-articles/122