论文标题
二进制复发，两者的力量正在区分模量
Binary recurrences for which powers of two are discriminating moduli
论文作者
论文摘要
给定一系列独特的积极整数$ w_0，w_1，w_2，\ ldots $和任何积极整数$ n $，我们定义了区分函数$ \ mathcal {d} _ {\ bf w} _ {\ bf w} modulo $ m $。 In this paper, we classify all binary recurrent sequences $\{w_n\}_{n\geq 0}$ consisting of different integer terms such that $\mathcal{D}_{\bf w}(2^e)=2^e$ for every $e\geq 1.$ For all of these sequences it is expected that one can actually give a fairly simple description of $ \ Mathcal {d} _ {\ bf w}（n）$对于每个$ n \ ge 1. $ $ $ $ $ $对于此类序列的两个无限家庭，这已经在2019年由Faye，Luca等人在2019年完成，分别是Ciolan和Moree。
Given a sequence of distinct positive integers $w_0 , w_1, w_2, \ldots$ and any positive integer $n$, we define the discriminator function $\mathcal{D}_{\bf w}(n)$ to be the smallest positive integer $m$ such that $w_0,\ldots, w_{n-1}$ are pairwise incongruent modulo $m$. In this paper, we classify all binary recurrent sequences $\{w_n\}_{n\geq 0}$ consisting of different integer terms such that $\mathcal{D}_{\bf w}(2^e)=2^e$ for every $e\geq 1.$ For all of these sequences it is expected that one can actually give a fairly simple description of $\mathcal{D}_{\bf w}(n)$ for every $n\ge 1.$ For two infinite families of such sequences this has been done already in 2019 by Faye, Luca and Moree, respectively Ciolan and Moree.
