Lucas序列中可被其指数整除的项
The terms in Lucas sequences divisible by their indices
摘要：
对于第一类Lucas序列（u_n）和第二类Lucas序列（v_n），通常定义为：u_n=（a^n-b^n）/（a-b），v_n=a^n+b^n，其中a和b是整数或共轭二次整数，本文描述了n整除u_n的指数集n和n整除v_n的指数集n.在早期工作的基础上，特别是Somer的工作，我们证明了这些集合中的数字可以写成一个所谓的基本数的乘积，它只能是1，6或12，以及特定的素数，这些素数被明确描述。对于每种序列，也给出了以这种方式出现的所有素数的集合的一些性质。
英文摘要：
For Lucas sequences of the first kind (u_n) and second kind (v_n) defined as usual for positive n by u_n=(a^n-b^n)/(a-b), v_n=a^n+b^n, where a and b are either integers or conjugate quadratic integers, we describe the set of indices n for which n divides u_n and also the set of indices n for which n divides v_n. Building on earlier work, particularly that of Somer, we show that the numbers in these sets can be written as a product of a so-called basic number, which can only be 1, 6 or 12, and particular primes, which are described explicitly. Some properties of the set of all primes that arise in this way is also given, for each kind of sequence.
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