We present a method for estimating the least common multiple of a large class of binary linear recurrence sequences. Let , , and be fixed integers, and let be the recurrence sequence defined by for all . Under some conditions on the parameters, we determine a rational nontrivial divisor for , for all positive integers and , such that . As consequences, we derive nontrivial effective lower bounds for , and we establish an asymptotic formula for , where is a fixed positive integer. Denoting by the usual Fibonacci sequence, we prove, for example, that for any , we have
where denotes the golden ratio. We conclude the paper with some interesting identities and properties regarding the least common multiple of Lucas sequences.
"On the least common multiple of binary linear recurrence sequences." Rocky Mountain J. Math. 51 (5) 1583 - 1597, October 2021. https://doi.org/10.1216/rmj.2021.51.1583