In this short note, we reprove in a very elementary way some known facts about Pisano periods as well as some considerations about the link between Pisano periods and the order of roots of the characteristic equation. The technics only requires a small background in ring theory (merely the definition of a commutative ring). The tools set here can be reused for all linear recurrences with quadratic non-constant characteristic equation.

翻译：在这个简短的注释中,我们以非常简单的方式对Pisano期的一些已知事实以及Pisano期与特性方程式根部顺序之间联系的一些考虑进行重新论证。技术员只需要环形理论中的小背景(仅是通货圈的定义 ) 。 这里设定的工具可以用二次非连续特性方程式重新用于所有线性重复发生。