论文标题
分类线性序列
Classifying linear division sequences
论文作者
论文摘要
我们对整数中的所有线性分割序列进行了分类，这个问题至少可以追溯到1930年代。作为推论，我们还将这些线性复发序列分类为$（x_m，x_n）= \ pm x _ {（m，n）} $的整数中。我们还表明，如果两个线性分裂序列经常有一个较大的公共因子，那么它们在某些算术进程上的共同线性分裂序列都可以分开。此外，我们的证明也适用于多项式。我们证明的关键是Ritt的不可约性定理和子空间定理（Schmidt和Schlickewei的子空间定理），朝Bugeaud，Corvaja和Zannier开发的方向。
We classify all linear division sequences in the integers, a problem going back to at least the 1930s. As a corollary we also classify those linear recurrence sequences in the integers for which $(x_m,x_n)=\pm x_{(m,n)}$. We also show that if two linear division sequences have a large common factor infinitely often then they are each divisible by a common linear division sequence on some arithmetic progression. Moreover our proofs also work for polynomials. The key to our proofs are Ritt's irreducibility theorem and the subspace theorem (of Schmidt and Schlickewei), in a direction developed by Bugeaud, Corvaja and Zannier.
