沿偶数幂采样的Fibonacci序列（几乎）是可实现的
Fibonacci along even powers is (almost) realizable
AI总结：
本文研究了Fibonacci序列沿特定幂次采样的可实现性，证明了沿奇数幂采样的序列不可实现，而乘以5后的偶数幂采样序列可实现，揭示了与判别式相关的算术现象。
摘要：
如果一个整数序列是某个映射的周期点计数，则称其为可实现的。Fibonacci序列$(F_n)$没有此性质，沿平方采样的Fibonacci序列$(F_{n^2})$也没有此性质。我们通过证明序列$(5F_{n^2})$是可实现的，表明这是一个与Fibonacci序列判别式相关的算术现象。更一般地，我们证明对于任意$k\ge1$，$(F_{n^{2k-1}})$在特别强的意义上不可实现，而$(5F_{n^{2k}})$是可实现的。
英文摘要：
An integer sequence is called realizable if it is the count of periodic points of some map. The Fibonacci sequence $(F_n)$ does not have this property, and the Fibonacci sequence sampled along the squares $(F_{n^2})$ also does not have this property. We prove that this is an arithmetic phenomenon related to the discriminant of the Fibonacci sequence, by showing that the sequence $(5F_{n^2})$ is realizable. More generally, we show that $(F_{n^{2k-1}})$ is not realizable in a particularly strong sense while $(5F_{n^{2k}})$ is realizable, for any $k\ge1$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
